"Lack of author or age of song do not make a genre. Musical style does"
Style does not - origins and process does.

OED defines genre thus Jim
'A style or category of art, music, or literature:'

I still think you're wrong on this one, my view is that origins and process makes the tradition, and the musical 'style' or 'form' is what evolves from that tradition. I know we are going to disagree on this one ;) but if you accept 'folk' as a genre, as we have to with the common understanding in today's society, then we are back to it being perfectly possible for a new song (or tune) that fits that style or form to be a folk song or tune.

John