I think Percy French also had something to do with "Mountains of Mourne": oh yes, he wrote the lyrics and Houston Collisson wrote the tune. So a song is not traditional unless no-one knows who wrote it, and it has been handed down at endless knees. But there are songs which are written in traditional style or have "gone into the tradition": and yes, there I'd agree that the lines are blurred.
As for "Star of the County Down", the tune goes back hundreds of years before Cathal MacGarvey wrote his set of lyrics, and has been used for at least 5 other songs and hymns that I can think of. "You can't put a good tune DOWN"!