And if folk is only a genre of music, where does that leave the concept of a living tradition?

I do NOT, however, believe that "every music is folk". Here, preserved for dubious posterity, is my definition of folk music from a previous thread.

"A folk song, to me, is a song with a strong (ie. readily hum-able) melody and intelligent lyrics, sang either with optional acoustic backing or unaccompanied. This may be a Traditional song (by which I mean an old song still widely sung and composed by somebody whose name is lost to posterity and thus credited to Trad); or it may be a song written by someone whose name is known and may be either dead or alive, however recent or otherwise. But the two most important identifying features of a folk song are a strong melody and intelligent lyrics."