"So... is it folk because it is so old nobody knows who wrote it?"
No, it's folk because the folk (the same people who used folklore and told folk tales as part of their everyday lives) in the first place, made the songs to reflect their lives, beliefs and values, then passed them on where they were remade again and again until their origins were forgotten and they bacame part of a culture of ordinary people.
The term folk was devised in the 1830s to define a specific body of lore, tales, music; and to distinguish from the written and composed culture passed on to us by 'our betters'.
It is this that was and continues to be documented and archived and it is this which will survive once all the clubs disappear up their own jaxies.
I've seen people come into folk clubs, set up music stands and sing and play everything from Gounod to Gershwin - was that folk?
"I have a recording of Frank Sinatra singing "First time ever I saw your face," And your point is....? First time ever isn't a folk song (not according to its composer anyway).
Incidentally - would love to get the details of 'First Time Ever' by Sinatra - didn't know he'd recorded it.
Jim Carroll