Trouble is, you cant really say "this set of words and tune IS a folk song". (sorry about the shouting capitals, cant do italics).You can only say "this set of words FUNCTIONS as a folk song in certain context"(or functioned, or might function in the future).
And you can say without fear of contradiction"the folk process at a certain time and place produced a body of music with certain recognisable characteristics". But you're making an unjustifiable leap if you go onto say "therefore a song with those characteristics is a folk song", because you've changed the definition of folk between the two statements. Which, of course we all do all the time, using the same word with subtly different meanings in different contexts. That's language for you.