Joe I quite like your idea that a tune/song needs history to become folkmusic. Much of that 60's material is way over a generation in age, but I would still label it contemporary out of deference to those that have researched and collected a huge body of "traditional"material.
Maybe I am not explaining it very well but I have a problem with below:
for it is the re-fashioning and re-creation of the music by the community that gives it its folk character. and oral transmission
Is this in reality sloppy transcription and lack of a pitch perfect ear as the song migrates through the community. We have many examples on this forum of lyrics being misheard when transcribed. It is very very easily done. There is a counter argument that once a song is collected it is effectively fossilised and further variance is frowned on.I would argue that today very little refashioning and re-creation(whatever that means) occurs. The dawning of electronics in everyone's hands further stifles evolution because a perfect copy can be captured. Additionally today there is a commercial aspect comes into play. Airtime is far more likely for popular tunes/songs and I would argue this had far more influence on the popularity of folk music in the 60's in the UK, than Peter the painter types in scruffy duffel coats gibbering in garrets.

Folk encompasses a broad church, why not celebrate this rather than trying to stitch it into little boxes that simply create argument.