There's a difference between saying a song is not of Irish origin, though that it is sonetimes erroneously thought to be, and saying that it is not in any way an Irish song, in spite of the fact that it has entered the oral repertoire of people who don't have a clue where it came from, or where they first heard it, and is sung all over the country.

Saying that it is in some sense a Irish song isn't the same as saying that it isn't just as much, or even more, at home elsewhere.