Andy, you've asked a very interesting question, one that I would be interested in discussing. But it will probably be impossible on this site. There will be far too much noise.
In general, for every one Mudcat post addressing the subject of the thread there are at least 20 posts by people who have no interest in the subject but simply have a lot of free time on their hands and a hopelessly vain desire to sound clever.
When the subject includes the word "folk," that ratio becomes much higher: for every one post addressing the subject there will be at least 50 posts by people who just dropped in to tell you that's not what "folk" means, despite the fact that 95% of the American public take it to mean the same thing as you take it to mean. They think they are something akin to the immortels of the Académie française, with the authority to dictate language and overrule common usage.
Michaelr is certainly on the right track. The songs that we call folk tend to be story songs, rather than, as Bob Dylan said, "tell your ma, tell your pa, our love's a-gonna grow; ooh wah wah."
But there's also a difference in the music. I don't know enough about music theory to describe it, but I can tell a folk song from a rock song without hearing the words, even if the latter is played on acoustic guitar and sung without a microphone. And I can spot a rock musician by his guitar style, even if he's playing a folk song.
It might not be the song itself, but only the manner of playing it. When George Strait sings "Red River Valley" (https://www.youtube.com/watch?v=PupeWwhMbQc), it sounds like a folk song, though most of his songs sound like country-western and not folk. But the Ventures did a rock version of it so trite and commercial that no one would have guessed it was based on a folk song.
One thing that might help the discussion (if we can weave it in between the noisemakers) would be to consider other examples like that, or songs that are on the cusp between folk and something else. I think even the pseudo-immortels would call "Red River Valley" a folk song, since they don't know who wrote it. But we could similarly discuss Stephen Foster's "Oh Susanna" or Jimmie Davis' "You Are My Sunshine."