Rob,
No-one with any basic knowledge of the tradition nowadays believes that knowing the origin of the song has any relevance at all to the oral tradition. The oral tradition is concerned solely with transmission, not origin, and rightly so IMO. How can a song be traditional one day and the next not be just because we discovered Martin Parker wrote it in 1652 or Harry Clifton in 1860 etc.?

The word 'traditional' can be applied to almost anything that is handed down, whether altered or not. Alteration is a characteristic, not a prescription. 'Rule Britannia' is very much part of several traditions including oral tradition, but it seldom gets altered. In its original form it's not a 'folk song' but it does form part of some folk songs.

The answer to your question is a complex one. Perhaps you need to define what your concept of 'traditional' is.