OK, Okay, Oll Korrect?

There's a bit in Someone Who'll Watch Over Me about the etymology of "OK". The character in the play says that no one has ever figured out the etymology of the common expression. I had planned today to search the internet and see what I could find. Imagine my surprise when I checked Kris' blog to find she has linked to an online etymology dictionary! Woo hoo!

Naturally, I looked up OK immediatey:

OK
1839, only survivor of a slang fad in Boston and New York c.1838-9 for abbreviations of common phrases with deliberate, jocular misspellings (cf. K.G. for "no go," as if spelled "know go"); in this case, "oll korrect." Further popularized by use as an election slogan by the O.K. Club, New York boosters of Democratic president Martin Van Buren's 1840 re-election bid, in allusion to his nickname Old Kinderhook, from his birth in the N.Y. village of Kinderhook. Van Buren lost, the word stuck, in part because it filled a need for a quick way to write an approval on a document, bill, etc. The noun is first attested 1841; the verb 1888. Spelled out as okeh, 1919, by Woodrow Wilson, on assumption that it represented Choctaw okeh "it is so" (a theory which lacks historical documentation); this was ousted quickly by okay after the appearance of that form in 1929. Okey-doke is student slang first attested 1932.

Let's see what else I can find by doing searches... wow. There's a lot out there on this!

Here's a few explanations.

I like this one:
-The previous explanation is connected with my favorite one, that says that during the Civil War, when batallions returned from the front, the first man in line carried a sign with the number of soldiers killed in action in that group. So the signs stated "9 Killed", "5 killed" and so on. If the number was zero, they stated "O K", a perfect mark.

Here's another discussion about the origin of OK.

What's very interesting to me is that I can't find the explanation given in Someone Who'll Watch Over Me anywhere! Did Frank McGuinness make it up? He claims that Stonewall Jackson created the word because he couldn't read or write and spelled all with an "O" and correct with a "K".