Christie Moore's the one who claims it as a Scottish song.

At any rate the traffic was two way, hence the naming of a type of tune as "highland" in Donegal. There's lots of Irish music that is genuinely Irish, lots of Scots music that originated in Ireland, England or even Italy, the same with English music, and one of the fascinations of traditional arts is trying to follow how various strands have moved between countries and even continents.