I recommend taking a look at G Malcolm Laws' books, Native American Balladry and American Balladry from British Broadsides. Also, The Ballad Collectors of North America by Scott B Spencer will give you some information on the history of folk song scholarship.
I think that the generally accepted definition of folklore is that it's informal artistic expression that takes place in a group. Thus, it follows that folk music is music shared informally. So my personal feeling is that one cannot say a particular song is a folk song. It's "folkiness," for lack of a better term, depends on the context in which it is performed or shared.