Robert Hendrickson, The Facts on File Encyclopedia of Word and Phrase Origins, fourth edition, (2008), observes that Pickwickian has come to be used in a number of not particularly consistent ways:
Pickwickian; Pickwickian sense; Pickwickian syndrome. Generally, Pickwickian means jolly, plump, and generous, after Mr. Samuel Pickwick, Esq., in Charles Dickens's The Pickwick Papers (1836–39). Dickens, as noted in the novel (chapter 35), took the name from Bath coach proprietor, whose name derives from the village of Pickwick in England: [quotation omitted] The immortal Pickwick's name is also remembered by Pickwickian sense, meaning a word used in a different than usual sense in order to avoid offending someone (see The Pickwick Papers, chapter 1, for a much fuller explanation). Pickwickian syndrome is a medical term for "an abnormality characterized by extreme obesity accompanied by hypoventilation and polycythemia." The character Joe in The Pickwick Papers suffers from the disease.
The elucidation of Pickwickian sense in chapter 1 of The Posthumous Papers of the Pickwick Club bears repeating at some length. In this chapter, Samuel Pickwick has been selected by the club he organized to pursue scientific and other studies on an extended road trip, and in accepting the assignment he alludes to the possible dangers of the journey:
"... Travelling was in a troubled state, and the minds of coachmen were unsettled. Let them [members of the Pickwick Club] look abroad, and contemplate the scenes which were enacting around them. Stage coaches were upsetting in all directions, horses were bolting, boats were overturning, and boilers were bursting. (Cheers—a voice "No.") No! (Cheers.) Let that honourable Pickwickian who cried "No" so loudly, come forward and deny it if he could. (Cheers.) Who was it that cried "No?" (Enthusiastic cheering.) Was it some vain and disappointed man—he would not say haberdasher—(loud cheers)—who, jealous of the praise which had been—perhaps undeservedly—bestowed on his (Mr. Pickwick's) researches, and smarting under the censure which had been heaped upon his own feeble attempts at a rivalry, now took this vile and calumnious mode of———
"Mr. BLOTTON, (of Aldgate,) rose to order. Did the honourable Pickwickian allude to him? (Cries of "Order," "Chair," "Yes," "No," "Go on," "Leave off," &c.)
"Mr. PICKWICK would not put up to be put down by clamour. He had alluded to the honourable gentleman. (Great excitement).
"Mr. BLOTTON would only say then, that he repelled the hon. gent's false and scurrilous accusation, with profound contempt. (Great cheering.) The hon. gent. was a humbug. (Immense confusion, and loud cries of "chair" and "order.")
"Mr. A. SNODGRASS rose to order. He threw himself upon the chair. (Hear.) He wished to know, whether this disgraceful contest between two members of that club should be allowed to continue. (Hear, hear.)
"The CHAIRMAN was quite sure the hon. Pickwickian would withdraw the expression he had just made use of.
"Mr. BLOTTON, with all possible respect for the chair, was quite sure he would not.
"The CHAIRMAN felt it his imperative duty to demand of the honourable gentleman, whether he had used the expression which had just escaped him, in a common sense.
"Mr. BLOTTON had no hesitation in saying, that he had not—he had used the word in its Pickwickian sense. (Hear, hear.) He was bound to acknowledge, that, personally, he entertained the highest regard and esteem for the honourable gentleman [Mr. Pickwick] ; he had merely considered him a humbug in a Pickwickian point of view. (Hear, hear.)
"Mr. PICKWICK felt much gratified by the fair, candid, and full explanation of his honourable friend. He begged it to be at once understood, that his own observations had merely been intended to bear a Pickwickian construction. (Cheers.)"
In this burlesque of Parliamentary controversy, we find the characterization "humbug"—as well as allusions to "false and scurrilous accusation," "some vain and disappointed man," "jealous," and "vile and calumnious"—ultimately rendered harmless and uninsulting as a consequence of being intended only in a Pickwickian sense, in a Pickwickian point of view, and with a Pickwickian construction.
William Benét, The Reader's Encyclopedia, second edition 1965) offers this discussion of "in a Pickwickian sense":
in a Pickwickian sense. Said of words or epithets usually of a derogatory or insulting kind that, in the circumstances in which they are employed, are not to be taken as having quite the same force or implication as they normally would have. The allusion is to the scene in chapter 1 [of The Pickwick Papers] where Mr. Pickwick accuses Mr.Blotton of acting in a "vile and calumnious manner," whereupon Mr. Blotton retorts by calling Mr. Pickwick a humbug. It finally is made to appear that both use the offensive words only in a Pickwickian sense and that each has, in fact, the highest esteem and regard for the other.
It thus appears that "in a Pickwickian sense" means not "in a sense that Mr. Samuel Pickwick would be likely to have in mind in using the expression in question," but "in a sense that one Pickwickian [that is, one member of the Pickwick Club] might use the expression in question in the course of discussion with one or more other Pickwickians."
Resort to "in a Pickwickian sense" thus has much in common with Touchstone's explication of "the peace-maker If" in As You Like It:
TOUCHSTONE. O, sir, we quarrel in print by the book, as you have books for good manners. I will name you the degrees. The first, the Retort Courteous ; the second, the Quip Modest ; the third, the Reply Churlish ; the fourth, the Reproof Valiant ; the fifth, the Countercheck Quarrelsome ; the sixth, the Lie with Circumstance ; the seventh, the Lie Direct. All these you may avoid but the Lie Direct ; and you may avoid that too with an If. I knew when seven justices could not take up a quarrel ; but when the parties were met themselves, one of them thought but of an If, as : 'If you said so, then I said so'. And they shook hands, and swore brothers. Your If is the only peace-maker ; much virtue in If.
Evidently, to say that an assertion under scrutiny is "perhaps even in some Pickwickian sense correct" is as much as to say that it is in some non-Pickwickian (that is, normal and unstrained) sense incorrect.