To revert to the original question, there seems to be no hard and fast rule over what might be regarded as 'folk' in the wider sense. Songs written in a style which reflects traditional styles seem to qualify without much disagreement (even from Jim!). Other songs seem to pass muster if they are performed in a recognisably 'folky' style (let's not discuss what that means!), even pop songs in some circumstances.

Established folk performers seem to be permitted a bit more latitude than mere floorsingers. I don't recall ever hearing Elvis covers, but Nic Jones would play Buddy Holly, in his own style of course. Swan Arcade did a cracking version of the Kinks' 'Lola'. June Tabor's version of 'Love will tear us apart' is approached no differently from her band's arrangements of both modern songs with a more folky pedigree or traditional ballads. Of course, in all these cases these form part of a much broader repertoire which included traditional songs.

It's an aesthetic judgement rather than something which can fall within a definition. What a performer can get away with will depend on the ethos of the club and the tastes of the audience. The same goes of course for treatments of traditional songs.

I think what is usually expected from such songs is that the lyrics should be intelligent (and intelligible) and make a point or carry a message, and often have a narrative. This would seem to rule out a lot of pop songs, no matter how they are performed.