"Traditional" has more than one meaning here. Traditional as it is defined in folk music circles, or traditional in that it is always done because it is part of the popular culture.

Habituation is an aspect - so many songs might simply be forgotten, written or not, so if they are rediscovered in print (author or not) are they now "traditional?" If it has an author and is in print but is so popular and sung with gusto on special occasions, does it become traditional because it fits a specific tradition or occasion? It isn't folk process traditional, but it is culturally traditional. Like Jingle Bells at christmas or Happy Birthday at your party.

SRS