Regardless of how revered a person does it, and legality notwithstanding, I think there's something dishonest about claiming you "wrote" or "composed" a melody when you actually lifted it wholesale or only slightly arranged it from a trad. source or one of the classical composers (who probably "borrowed" heavily from tradition, too). If you modify lyrics or write new ones or do a unique arrangement, I have no problem with your version being copyright protected. I'm even pretty much OK with someone finding a truly obscure folk song and taking out a copyright on it. (If you don't, and you record it, somebody else may claim ownership and prevent you from using it, can't they?)
I just don't understand why a song like "Fare Thee Well" isn't presented as "Music: traditional English song; Lyrics: Bob Dylan, based on the trad. English song 'Leaving Of Liverpool;' © Bob Dylan." This seems more honest than "words and music by Bob Dylan."

FWIW, while Woody did this all the time, too, at least he publicy invited anyone and everyone to sing, share "his" songs, print the lyrics out, etc. So does John Prine. Dylan's attitude about his copyrights is quite another story.