The silliness of the whole argument becomes clear when one substitutes "tune" for "song".

Plenty of people are composing new jigs, reels, hornpipes etc. all the time. Are these compositions not "folk"? To which the answer can only be:

"Of course they are; don't be daft."

Music is folk music if it sounds like folk music; i. e. if it uses the familiar language: the folk idiom, as it were.

End of discussion. Now run along and play some music.