A look at two recent editions of popular U.S. dictionaries indicates that they do not explicitly recognize "scratch my back and I'll scratch yours" or "do me a favor and I'll do you a favor" as a distinct meaning of "quid pro quo."
Here is the entry for "quid pro quo" in Merriam-Webster's Eleventh Collegiate Dictionary (2003):
quid pro quo n {N[ew] L[atin], something for something} (1582) : something given or received for something else; also : a deal arranging a quid pro quo
And here is the corresponding entry in The American Heritage Dictionary of the English Language, fifth edition (2010):
quid pro quo n., ... Something that is given in return for something else or accepted as a reciprocal part of an exchange. ...
Nothing in these definitions points to a distinct implicit notion of kickbacks or pay-to-play or emoluments for favorable policy, although one could park such an idea in the broad contours of the expression, just as one could in the term reciprocity. But they do put the notion of "something of value for something else of value" squarely at the center of the term's meaning in English.
The most plausible explanation of why this meaning emerged victorious in English but not in Italian, I think, is that English usage derives primarily from the expression's meaning in one learned profession while Italian usage derives primarily from its meaning in another.
'Quid pro quo' in law
Use of quid pro quo to indicate an exchange of things of value goes back quite far in English law. Henry Black, A Dictionary of Law: Containing Definitions of the Terms and Phrases of American and English Jurisprudence, Ancient and Modern (1891) offers this brief discussion of the term:
QUID PRO QUO. What for what; something for something. Used in law for the giving one valuable thing for another. It is nothing more than the mutual consideration which passes between the parties to a contract, and which renders it valid and binding. Cowell.
And Giles Jacob, A New Law Dictionary Containing the Interpretation and Definition of Words and Terms Used in the Law, fifth edition (1744) has this:
Quid pro quo, Signifieth what for what; and is used in the Law, for the giving of one Thing of Value for another Thing, being the mutual Consideration and Performance of both Parties to a Contract. Kitch. 184. And as this is the Consideration of a good and binding Contract or Bargain: So that which is contrary to it, is what the Law calleth Nudum pactum ["naked promise"]. 5 Rep. 83. Dyer 98.
Elsewhere in the same dictionary, Jacob defines consideration as "the material Cause or Quid pro quo, of any Contract, without which it will not be effectual or binding." And in explaining the nature of a binding contract, he says this:
As if a Man sells his Horse or other Thing to another, for a Sum of Money ; or covenants, in Consideration 20 l. to make him a Lease of Farm, &c. these are good Contracts, because there is a Quid pro quo, or one Thing for another : But if a Person make Promise to me, that I shall have 20 s. and that he will be Debtor to me therefore, and after I demand the 20 s. and he will not give it to me, yet I shall never have any Action to recover this 20 s. because this Promise was no Contract, but a bare Promise, or Nudum Pactum ; though if any Thing were given for the 20 s. if it were but to the Value of a Penny, then it had been a good Contract.
It thus appears that the English legal system was so mistrustful of "something for nothing" that it made "something for something" the cornerstone of its contract law.
Stepping back farther still, Thomas Blount, Νομο-λεξικον: a Law-Dictionary (1691) has this entry for the expression:
Quid pro quo, Is an artificial speech, signifying as much as the Greek συναλλαγμα [exchange] among the Civilians, which is a mutual performance of both parties to a Contract, or a giving one thing for another, as 10 l. for a Horse, Kitchin fo. 184.
And here is Blount again in Glossographia: or a Dictionary, Interpreting All Such Hard Words (1656):
Quid pro quo, is an Artificial Speech in our Common Law, signifying as much as the Greek συναλλαγμα [exchange], among the Civilians, which is a mutual Protestation or performance of both parties to a Contract ; as a Horse and Ten pound, between the buyer and the seller. Kitch. fol. 184. And used in our common Speech, One for another ; as to render one Quid pro quo, i. to give him as good, as he brings. And is used by Apothecaries, when, instead of one thing, they use another of the same nature.
So in 1656 Blount views the expression as a "hard word" and yet notes that it has leaked from the English Common Law into common speech, as well as emerging in the discourse of apothecaries. The "Kitch," or "Kitchin" mentioned in various law dictionary entries may be John Kitchin, an English judge who wrote the book Jurisdictions and who died in or before 1588.
Edward Coke, The First Part of the Institutes of the Lawes of England (1628):
And the reason of this [rule requiring an exchange of things of value between a lessor and a lessee] is, for that in euery contract there must be quid pro quo, for contractus est quasi actus contra actum, and therefore if the Lessor hath nothing in the land, and the Lessee hath not quid pro quo not anything for which he should pay any rent. And in that case he may also plead, that the Lessor non dimisit, and giue in euidence the other matter.
W.G.'s 1651 translation from the Latin of John Cowell, The Institutes of the Lawes of England (1605) has this commentary (starting on page 184) in section 4 of a chapter titled "Of obligation by words":
4. But it is to be observed, that this verball Obligation is called a simple contract, (f) by our Authors, who weigh that which is done (g) more strictly then the definitions of things and that they do not bind, unlesse there be as consideration, or a quid pro quo, (h) as where a promise is the occasion, that any one doth [t]hat which otherwise he is not obliged unto.
A sixteenth-century instance of "quid pro quo" in a legal setting appears in William Lambarde, A Perambulation of Kent: Conteining the Description, Hystorie, and Customes of That Shyre (1576/1596):
And in my simple iudgement, it is not fit that this Custome [allowing minors to sell land that they inherit] should be construed by equitie, to enable an Infant, of little discretion, and lesse experience, to sell his lande, and not to prouide whithall that hee should haue, Quid pro quo, and some reasonavble recompence for the same : for that were not to defend the Pupill and Fathrlesse, but to lay him wide open to euerie slie deceipt, and circumuention.
But the oldest instance of "quid pro quo" in a legal context and in a book written predominantly in English is from Christopher St German, The Dialogve in English, betweene a Doctor of Diuinitie, and a Student in the Lawes of England (1528/1604):
If hee to whom the promise is made, haue a charge by reason of the promise which [he] hath also performed: the[n] in that case he shall haue an action for that thing that was promised though hee that made the promise haue no worldly profit by it.Asa if a man say to an other, heate such a poore man of his disease, or make an high way, and I that giue thee thus much, and if he do it, I thinke an action lyeth at the common law. And moreover though the thing that he shall dobe all spirituall, yet if he performe it, I thinke an action lyeth at the common Law. As if a man say to an other fast for me through Lent, and I shall giue the xx.poundes, and he peformeth it, I thinke an action lyeth at the common Lawe. And in likewise if a man say to an other, marry my daughter and I will giue thee xx. pounde, upon this promise an action lyeth, if hee marry his daughter, and in this case hee cannot discharge the promise though hee thought not to be bound thereby, for it is a good contract, & he may haue Quid pro quo, that is to say, the preferrement of his daughter for his money.
St. German's book was originally published in 1528 but went through many subsequent editions. St German died in 1540.
'Quid pro quo' in medicine
The use of "quid pro quo" in medicine, as mentioned in the entry for the term in Blount's Glossographia (1656) noted above, is also quite old. From a 1535 translation of Desiderius Erasmus, A lytle treatise of the maner and forme of confession:
These persones do not thynke, that they do cōmit thefte yf they do fynyshe the worke that they haue taken in hande foure dayes space whiche they myghte haue made an ende of in one day: and in the meane while, they be fedde with another mānes meate and take theyr whole wages for euery daye accordynge to promyse and couenaūt. Neyther do they thynke that they make any lye whan they do promyse that they wyll do that thyng whiche they do not perfourme: and how do they (trowe you) excuse their leasyng? this is a poynt (say they) of our occupatio &; crafte: Naye, it belogeth to theyr occupation, truely and faythfully to do that thynge whiche theyr crafte promyseth to be done and not to lye or steale: but yet poticaries and phisions do more greuously offende than do these persones now rehersed which haue a prouerbe amonge them, quid pro quo, one thynge for another: they do otherwhyles sell this thynge, for that thyg they do minister stuffe that is rotten, and without any vertue or strengthe yea &; nowe hurtfull in steade of remedy and helpefull medecine: the byer asketh for rebarbarum and they do gyue hym rebarbarum aboue fortye yeres olde: there is no spice no gumme not onely there is no roote none herbe of so durable and vertue and strengthe but in longe processe of tyme, the vertue of it wyll be quite gone & lost. But they do say yf we dyd not mengle olde stuffe and newe together & so vtter the one with the other we shulde els be starke beggers & myghte famyshe, for all our occupatiō. I say, it were euyn better also to die than vnto thy sicke brother (whom yu oughtest euyn freely without money to succour) for to ministre that thyng, whiche shall augmēt and encrease his disease yea or para∣uēture also be cause of his dethe. The defaulte & offence of the po∣ticaries, redoūdeth also to ye phisicions.
From "The Apothicaries rules" in William Bullein, Bulleins bulwarke of defence against all sicknesse, soarenesse, and woundes that doe dayly assaulte mankinde (1562/1579):
xii. That he neither increase nor diminish the Phisicions bill, and kepe it for his owne discharge.
xiii. That he neither buy nor sel rotten drugges.
xiii. That he peruse often his wares, that they corrupt not.
xv. That he put not in quid pro quo, without aduysement.
Another early and interesting instance of the term, used in the sense (as Blount points out) of substituting one medicinal preparation for another with supposedly similar properties, appears in John Securis, A Detection and Querimonie of the daily enormities and abuses comitted in physick, concernyng the thre parts therof: that is, the physitions part, the part of the surgeons, and the arte of poticaries (1566):
Moreover he [a "poticarie"] shal not commit any crime or fault, either for loue or fauoure, or for hatred or feare: nor he may not be seduced by money or led by ignorance. Neither shal he geue at any time any poyson, or thinges procuring abortion, any thing that is to olde or out of use, thinges altered and sophisticate, or any quid pro quo. But he shall aske counsell (as often as nede shal require) pf a well learned phisition, what simple or compounde medycyne is to be substytuted and taken, for lacke one of the other.
From John Gerard, The Herball or, Generall Historie of Plantes (1597):
But concerning the faculties, Mathiolus saith, that all the Phisitions and Apothecaries in Bohemia vse the roots of this Oxe eie in steed of those of blacke Ellebor, namely for diseases in cattell: but he doth not affirme that the rootes heereof in medicines are substitutes, or quid pro quo; ...
From Francis Bacon, Of the Proficience and Advancement of learning, Divine and Humane (1605):
In the consideration of the Cures of diseases, I finde a deficience in the Receipts of propriety, respecting the particular cures of diseases : for the Physitians haue frustrated the fruit of tradition and experience by their magistralities, in adding and taking out and changing Quid pro quo, in their receipts, at their pleasures, commanding so ouer the medicine, as the medicine cannot command over the disease: For except it be Treacle and Mythridatum, and of late Diascoridum, and a few more, they tye themselues to no receipts seuerely and and religiously : for as to the the confections of sale, which are in the shoppes, they are for readinesse, and not for proprietie : for they are vpon generall intentions of purging, opening, comforting, altering, and not much appropriate to particular diseases ; and this is the cause why Emperiques, & old wome[n] are more happy many times in their Cures, then learned Phisitians : because they are more religious in holding their Medicines.
In this extract, Bacon uses receipts in its sense of "recipes."
'Quid pro quo' in politics and society
An early use of "quid pro quo" outside the fields of law and medicine appears in the course of a tedious religious polemic by N.D., An examen of the calendar or catalogue of protestan saincts, martyrs, and consellors, deuised by Ion Fox (1604):
Yow shall heare his [Sutkliffe's] owne words immediately following in the same matter. Nay (saith he) Scotus seemth rather to dislike Transubstantiation then otherwise. Behold here the trew dealinge of M. Sutkliffe who giueth vs quid pro quo as Apothecaryes are wonte. He should haue proued that Scotus determined in his resolution against the reall presence, and now he saith that Scotus seemeth rather to dislike Transubstantiation then otherwise. So as for the reall presence, heere is thrust in Transubstantiation, and for determination and resolution is shuffled in a seeminge to dislike rather then otherwise. Was there euer any such good Apothecary that gaue quid pro quo?
The "quid pro quo" here is clearly the substitution for one claim or argument with a weaker or otherwise less suitable one, explicitly on the model of an apothecary substituting whatever happens to be in the shop for what the physician called for. The striking thing here is that the quid pro quo replacement is of one thing with another (in this case, another of inferior quality), not an exchange of things of theoretically equal value (as in the legal sense). It is thus a usage in the tradition that seems to have won out in Italian but ultimately died out in English.
Also interesting—as an early example of the potentially unsavory connotations of "quid pro quo" in the "value for value" sense—is this example from a 1639 translation by T.C. of Jean-Puget La Serre, The Mirrour Which Flatters Not:
Others they say but Sculke, or lye i' th' lurch, / As we hold Schismaticks from the true Church, / So hold they all, that doe decline their way, / Nor sweare by Heaven, Al's excellent they say, / Twere well the'd see the fing'ring on these frets, / Can neither save their Soules, nor pay their Debts / Or would they think of Death as they should doe, / They would live better, and more honourd too. / Tis base to doe base deeds, yet for falkse fame, / To Kepe a stirre, and bustle into Name: / Whilst each applauds his owne, contemnes an others, / Becons his owne deserts, but his he smothers, / They feare Fame's out of breath, and therefore they, / Trumpet their owne praises in their owne way. / Or ioyne in Tricke of Stale Confed'racy. / Cal’d Quid pro Quo, Claw me, and Ile claw thee / Marry, at others (Tooth and Naile) they flye / That do not tread their Path, but would goe bye.
The preceding example is the earliest one I've found that use "quid pro quo" to describe a situation that specifically involves dishonest behavior.
And here is an example of the phrase in a political context, from James Howell, Dendrologia: Dodona's grove; or, The vocall forrest (1640):
The golden chaine of policy hath beene alwayes held to be, That the defense of a kingdome is the office of the Prince the honour of the Peeres, the service of the Souldier, and the charge of the subject, for Qui sentit commodum, sentire debit & onus.
Adde hereunto, that alleageance is an act of reciprocation ; as it bindes the King to protect, so it ties the subject to contribute, and by this correspondence there is a quid pro quo.
Assessment and conclusions
The phrase "quid pro quo" has appeared in texts written otherwise mostly in English for at least 490 years. The earliest example I found was from 1528, but I would not be at all surprised if even older examples exist.
The earliest examples of "quid pro quo" in English come arise in two distinct contexts: law (no later than 1528) and medicine (no later than 1535). And critically, the sense of the phrase "something for something" differs in the two fields.
In English common law, the sense of "quid pro quo" from its earliest days has amounted to "value for value"—that is "something for something" in contradistinction to "something for nothing." This conception of "quid pro quo" thus became a foundational requirement for a legally binding contract, a way of distinguishing an exchange from a gift or a theft.
In medicine, on the contrary, the sense of "quid pro quo" was "a makeshift substitute for something originally specified." The earliest published example of this usage in English is a translation of a treatise by Erasmus, who writes in 1535 that "quid pro quo" is a proverb among apothecaries in the Netherlands (and perhaps throughout Europe) to justify selling one drug or treatment in place of another. That learned observers viewed this practice with extreme suspicion is evident from Erasmus's description of its practical dangers and by the inclusion in William Bullein's "Apothicaries rules" in 1562 of a rule that the apothecary explicitly advise the buyer anytime the medicine being supplied was quid pro quo.
It is easy to see how these contrasting traditions of use for the same phrase might yield secondary meanings that are quite unlike each other. The legal "value for value" sense of "quid pro quo" invites subsequent use in the sense of "scratch my back and I'll scratch yours" or (more invidiously) "give me an unfair advantage on some project of importance to me, and I'll make sure that you are richly rewarded." The medical "best substitute available" sense, meanwhile, might predictably devolve into "whatever substitute I choose"; and if (as seems likely) the substitute is inferior to the originally prescribed item at treating the condition for which it was prescribed, it is easy to see how the inferior thing might be associated with misunderstanding or error.
In this regard, a snapshot of French usage of "quid pro quo" in 1611 seems quite revealing. Randle Cotgrave, A Dictionarie of the French and English Tongues (1611) provides three definitions for the phrase as used in contemporaneous French:
Quid pro quo. A palpable mistaking, a grosse error, one for another.
French in 1611 still had the baseline "one for another" meaning in play—but the tenor of the expression is undoubtedly colored by the other two meanings: a mistake and a gross error. I conjecture that these negative senses of "quid pro quo" arose from the apothecaries' proverb, because the consequences of that proverb lend themselves to deception and error. Just as significantly, French had no countervailing sense of "quid pro quo" as an exchange of things of presumed equal value voluntarily agreed upon by the contracting parties.
To my mind, the likeliest explanation for the divergence between Italian "quid pro quo" as misunderstanding and English "quid pro quo" as mutually advantageous arrangement is that Italian, like French, embraced the term through its medical/apothecary tradition whereas English ultimately abandoned that tradition of use in favor of the English common law sense of the term.