Lots of gray area potential here. I wouldn't consider "Redwing", "Dixie", "Old Zip Coon", "Wildwood Flower/Twine Mid the Ringlets", etc. traditional because they have known authors and were written by professionals as commercial "pop" music. On the other hand, they have endless variants, are rarely--these days, at any rate--learned from the original printed sources, and may or may not resemble any more what the composer intended. Of course, lots of even older songs, whether or not the authors are known (I think "Golden Vanity" et al. fit into this category), were also intended to be marketed, either in printed or oral form, to a mass audience. However, there are lots of "traditional" songs with known authors--the fiddle tune "Elzic's Farewell" comes to mind--that were not necessarily written by professional songwriters or intended to be printed/recorded and sold on a widespread basis. After all, I've known lots of musicians (from professional to strictly hobby) who composed tunes simply because they liked them.

Along with "Ookpik", "Ashokan Farewell", and "Rolling Home", a lot of people I know were mistaken about "Midnight on the Water" and "Aragon Mill". Of course, there are probably lots that I currently think are traditional about which I am STILL mistaken.