Exactly so, tunesmith. A quick survey of the field shows the classical guitar being used for all kinds of music in addition to classical. It's as versatile as the piano.

When I first started playing the "classic" guitar (circa 1955), people with more that just a passing acquaintance with guitars knew what you meant by "classic guitar." Technique books for the instrument (e.g., Classic Guitar Technique Vol. I, Vol. II, etc., by Aaron Shearer, and numerous others with such titles as How to Play the Classic Guitar) used that designation. Despite this widespread usage, I believe PoppaGator's post of 30 Jun 08 - 04:04 p.m. speaks to the point if on wishes to avoid confusion. "Classic" does seem to be a fairly broad term in its application. This is why, within recent years, I have taken to using the term "classical" when referring to the acoustic, wide-necked, nylon-strung guitar. But that still doesn't always solve the problem.

As to the matter of the wide neck making fretting strings with the left thumb difficult, this is a whole different discussion, and it doesn't remove the classic(al) guitar from being perfectly usable as a folk instrument.

Use of the left thumb to fret bass strings is not an ordained part of what might be called "folk technique." There are all kinds of "folk techniques." I have been playing folk song accompaniments on a classical guitar since the aforementioned 1955 and I've never had an occasion when I needed to use my left thumb to fret a string. But since I use the thumb, index, middle, and ring fingers of my right hand, I rarely play full 6-string chords. In the meantime, my left-hand fingers have room to operate without tripping over each other.

Others' mileage may vary.

Don Firth