Baloney. The etymology of OK was masterfully explained by the distinguished Columbia University professor Allen Walker Read in a series of articles in the journal American Speech in 1963 and 1964.
The letters, not to keep you guessing, stand for “oll korrect.” They’re the result of a fad for comical abbreviations that flourished in the late 1830s and 1840s. Read buttressed his arguments with hundreds of citations from newspapers and other documents of the period. As far as I know his work has never been successfully challenged.
The abbreviation fad began in Boston in the summer of 1838 and spread to New York and New Orleans in 1839. The Boston newspapers began referring satirically to the local swells as OFM, “our first men,” and used expressions like NG, “no go,” GT, “gone to Texas,” and SP, “small potatoes.”
Many of the abbreviated expressions were exaggerated misspellings, a stock in trade of the humorists of the day. One predecessor of OK was OW, “oll wright,” and there was also KY, “know yuse,” KG, “know go,” and NS, “nuff said.”