"Suppose that we reserve the T-word for songs of unknown authorship, which have survived generations of oral transmission. And suppose that we then apply the F-word to songs - whatever their origin - that the people of a specific community sing regularly, and acknowledge as their own."

As Malcolm Douglas ably pointed out recently (on another thread, I think) the question of authorship doesn't come into it. Any song can become 'traditional' if it is sung by a particular type of community over a long enough period.