Q #1: Should it be 'been usually' or 'usually been'?
I prefer "This quote has usually been credited to X" to "This quote has been usually credited to X," but I'm not aware of any valid rule of grammar that requires one or the other. In the bad old days of rampant prescriptivism, I believe, certain grammarians (such as Alexander Bain, in English Composition and Rhetoric: A Manual ) would have argued that the only proper way to word the sentence would be to put the modifier in front of "has been credited":
This quote usually has been credited to X.
But such strictures have been abandoned and forgotten, and today no narrow rule governs the particular placement of adverbs as Bain's once (supposedly) did. You are free to choose the order that best pleases your eye and ear.
Q #2: Whom should we ideally credit a quote to, in case there is a discrepancy?
I think that a suitable answer to this question requires a serious investigation of the quotation under scrutiny. I discuss the results of my investigation into the supposed Churchill/Wooden/ Budweiser quotation below, followed by a brief paragraph showing how I would word the attribution of the quotation in that particular case.
The [Yale] Dictionary of Modern Proverbs (2012) has this entry covering the gist of the quotation:
Success is never final (and failure is never fatal).
1920 George Starr White, Think (Los Angeles: for the compiler) 73 (the book is a collection of sagacious sayings): "Success is never final." 1954 "What Is Failure?" Coronet 36, no. 3 (Jul.) 70 (a small collection of sayings): "Success is never final and failure never fatal. It's courage that counts" (credited to George F. Tilton). DAP 571(27); RHDP 306. Cf. the somewhat older proverb "Failure is never final (is not forever)."
Sure enough, George Starr White, Think: Side Lights, What Others Say, Clinical Cases, Etc. (1920) includes this very brief apothegm:
Success is never final.
On the other side of the coin, we have this observation from The Homeletic Review, volume 93 (1927):
So, going on the supposition that you and I will never be Lord Chancellor or bishop of London or captain of the artillery, on the supposition that we are just average folks who, in the judgment of posterity were failures, let us solace ourselves with three considerations which I suggest for our comfort this morning. These three considerations are as follows: Failure is not Fated; Failure is not Futile; Failure is not Final.
And finally, from Amos Wells, "Little Sermons for Nurses," in Nurse (January 1916), we have the last piece of the famous attributed quotation:
This is the courage that counts, not the stolid courage of the stupid man, but the quivering, understanding courage of the sensitive man, who knows what is involved in the fight, but still fights on.
And to similar effect, from Alfred Barrett, "Good Courage: Story Sermon for the Children," in The Expositor (October 1919):
Put your faith in Jesus, be faithful in all things, seek the help of God—pray for strength in the trying hour. It is courage that counts in these days and it will also count in the life to come. "Be of good courage and he will strengthen your heart."
Both Forbes (1948) [snippet view] and Franciscan Message, volume 3 (1949) [snippet view] have this form of the combined quotation, attributed to George F. Tilton:
Success is never final and Failure never fatal. It's courage that counts.
—George F. Tilton
However, an anonymous placard is cited as bearing the same sentiment, in a union chapter update from Washington, D.C., by C.C. Hogan, in Trans-communicator, volume 61 (1944) [snippet view]:
In closing for this issue [I] would like to leave a little thought with you all I saw posted in a cafe about a year ago. It reads as follows: "Success is never final, failure is never fatal. It's COURAGE that counts."
An even earlier instance (also anonymous) appears in National Association of Ice Industries, Official Proceedings of the Twenty-Second Annual Convention (1939) [combined snippets]:
It is going to take a long time. It is a tough job. It can't be done alone. It is a challenge to youth as well as to age and experience. We must find contentment in the thrill of action. We must realize that success is never final and failure never fatal.
Despite the many published works that credit Winston Churchill with authorship of the proverb, I haven't found any that locates it in one of Churchill's many (and lengthy) written works. Moreover, the earliest association of any kind that I could find between the quotation and Churchill was a not-at-all scholarly attribution from 1965 (the year Churchill died). From The Louisville & Nashville Employes' Magazine, volume 41 (1965) [snippet view]:
Success is never final and failure never fatal. It's courage that counts.
This scrawny tree isn't much to hang Churchill's hat on. One of the laws of literary mythmaking is that eventually all memorable sayings get attributed to a small number of cultural icons (Confucius, Franklin, Lincoln, Twain, and Churchill among them); but the fact that such attributions tend to be factually unjustified means that unusual caution is appropriate in vetting those claims. In my view no substantial corroborating evidence exists in support of Winston Churchill as the author of the cited saying—and precious little for George Tilton as the author either.
It would hardly be surprising if the originator of the phrase had simply cobbled together three already-extant component proverbs. In any event, I see no reason to assign it to anyone when so little evidence of precisely where it came from and when is currently known. If forced to refer to Churchill at all, I would frame the discussion of attribution as follows:
The original source of this quotation is unknown, though it has often (on scant evidence) been attributed to Winston Churchill or to George F. Tilton. The earliest confirmed sighting of the quotation as rendered above was in the form of a window placard seen in 1943; and the earliest version to include both the "success" and "failure" pieces of the quotation but not the "courage" component appeared at a National Association of Ice Industries convention in 1939.