As Don Firth has said, a folk song is defined by the process it passes through.
It doesn't matter how or in what style it was made, the fact that it reflects enough of the experiences and emotions of enough people for it to be taken up and re-made so that it becomes as relevant to them as it was to its maker(s) gives it its 'folkness' and guarantees its transmission through time and distance.
I don't agree with Ron's comments on changing modes of transmission. The oral way the songs were passed on guaranteed a flexibilty, a looseness of form which allowed singers to re-make the songs so that Barbara Allen could have come from Scarlet, Scarborough, Reading, Edinburgh.... wherever Town, and the poor feller (or woman) dying from clap could equally be a soldier, sailor, marine, cowboy, whore.... whatever.
Ballad scholar, David Buchan's (flawed) theory that ballads had no set text, just plot and commonplaces, has some validity in our experience. We found that if you re-recorded the same song from a singer on a number of occasions over a period of time, you ended up with numerous versions; he or she re-made the song at each singing - this was particularly true of non-literate Travellers.
Modern songs come into the world in their 'ur' versions; they are fixed by their method of transmission rather than altered and adapted by it. New songs will always belong to the composer, Paxton, Dylan, McTell, electronic transmission, recording methods, printing, literacy, etc., have made sure of that, and to be doubly certain, the song-makers more often than not put a little (c) next to it so it can never belong to the 'folk' or anybody else (unless they sell it - I think I'm right in saying that The First Time Ever now belongs to the Michael Jackson estate).
Jim Carroll