Having consulted the definitive reference work on this subject (yes, there is such a thing: "The F-Word" by Jesse Sheidlower, published by Random House in 1999), we feel confident in dismissing the above claims as imaginative bunk. (Fornication Under Consent of the King, For Unlawful Carnal Knowledge)
The word "f" did not originate as an acronym. It crept, fully formed, into the English language from Dutch or Low German around the 15th century — it's impossible to say precisely when because so little documentary evidence exists, probably due to the fact that the word was so taboo throughout its early history that people were afraid to write it down. (The American Heritage Dictionary says its first known occurrence in English literature was in the satirical poem, "Flen, Flyss" (c.1500), where it was both disguised as a Latin word and encrypted — "gxddbov," deciphered as "fuccant," pseudo-Latin for "they f.")