I always thought that anonymous meant "Of unknown or undeclared source or authorship".

That sounds reasonable to me but I was not aware "anonymous" was a criteria for songs or tunes getting into oral traditions. Are you explaining to me that if, I don't know Planxty Irwin, had been passed down from my great grandfather to my grandfather and you recorded it as learned from my father and we later learn it was written by Carolan that the tune wouldn't have entered an oral tradition after all?