Slang words tend to produce loads of folk etymologies that have little basis in reality. Partially, this is because slang words tend to be less visible in records that survive to the modern time. And also partially, etymology tends to be a field where people feel inclined to make stuff up that sounds right and these stories get passed along because feeling right is valued more highly than actually being right.
The proposed etymologies of OK fall into three main buckets:
* OK is an initialism for a misspelled variant of 'all correct'
* OK is a phonetic rendition of some phrase in $LANGUAGE (there are a few different such languages proposed)
* OK is an initialism for some phrase in $LANGUAGE (again, different phrases in different languages have been proposed)
Of these etymologies, the second bucket can be pretty thoroughly ruled out immediately: OK shows up in our sources first as an initialism, not 'okay', so it's not likely to be anything other than an initialism. As for deciding what it's an initialism of... well, "all correct" is actually the most reasonable on first guess because someone who is going to come up with a "just-so" story for a folk-etymology is likely to go for a phrase which actually initializes to OK rather than one which conspicuously doesn't, and thus someone advancing an "all correct" theory is likely to be able to point to evidence of its truth. Which we have.