I have been told that when Si Kahn's son was visiting in Northern Ireland, he and a companion passed a pub and heard Si's song "Aragon Mill" being sung, and when Kahn asked about it, he was told it was a traditional song of Northern Ireland called "Belfast Mill."
I have also heard Dick Holdstock and Alan MacLeod tell of singing "Molly, Come Fare Away" in a very nice country-inn type restaurant, somewhere in the southern mountains, and having a woman who had dined there come up to them and say, "I never heard that song sound like that." Alan says she mentioned the Scot accent and he said something to the effect that it is a Scottish song so of course it sounds Scottish, and the woman said something about it just sounded odd to her. He then realized he actually knew little about the song, so asked the woman what she knew about the song. She said, "I wrote it." It is a great story; Jean (kytrad), is it true?
Dougie MacLean's song "Caledonia" was taken for traditional by the big corporation that used it in their advertising, who then were required by law (and a suit?) to pay him handsomely for it.
For a writer of tradition-based songs, to have your own work be taken for traditional, as in old, must be the ultimate compliment/validation, though not particularly helpful economically.
There is substantial slippery-slope potential here, though. Might calling something "traditional" be a way to avoid giving credit or royalty? And the point is well taken about songs "becoming" traditional. We know the source of, for example, lines in Shakespeare's plays, but some of these have certainly become traditional English-language expressions. Many songs of the 20th century (many mentioned above) have writers still known but have clearly entered "The Tradition." I have heard it said (by Rick Fielding and others) that a song becomes traditional when we no longer remember who wrote it, which of course means some singers make songs traditional faster than others...