There's a huge difference between songs that "everyone knows" because they sing them or hear them sung and songs that "everyone knows" because they're on the radio all the time.

No there isn't; in terms of human experience & meaning there is no difference whatsoever.

And those songs won't change. Unchained Melody will always be Unchained Melody, and 500 Miles will always be 500 Miles. Folk songs are different, because they're produced differently, transmitted differently and preserved differently.

The songs change with every performance, every spin, every remix, every dance because the experience will always be of the moment. These are Folk Songs in the sense that they are known to the folk, cherished by the folk; they have meaning, function, purpose and relevance whatever differences you might wish to fantasise over - or yet the origins of such specious (and redundant) criteria in the first place. But as I've demonstrated elsewhere, the 1954 Definition is so nebulous as to be useless in defining anything other than - er - music. Anything else is determined by your (evidently impoverished) personal faith.   

All we're arguing about - well, all I'm arguing about - is a label.

And since when has Folk Music ever been just a label? We're talking about the essentials of music in relation to human community & life experience, not some pseudo-academic taxonomy which was all so much bullshit anyway.   

I can appreciate an acoustic night or a covers band or an MC crew or whatever without feeling the urge to say that they're singing "folk songs". God knows they don't think they're singing folk songs - they'd probably find it more of an insult than a compliment.

Folk Music is about context, function and usage. When people say There is no Folk Music, then I say of course there is - and I point to it, and I say why it's folk music. Not Folk in terms of some antiquarian fantasy genre, or, worse still, label, which really would be insulting - rather Folk in terms of a living, breathing enthnographic reality of human life which we might look at along with all World Folk Musics and be justly proud. Even if it is just people dancing to some old 78s in the local community centre, or the local covers band, or the local Drum & Bass crew, or the local Irish band, or the local Brass Band, or Choral Society, or even Folk Club, who like most folk singers got all their songs off records anyway.