Afraid that's par for the course, Alan. There are dozens, possibly hundreds, of songs that are listed as "Irish" which aren't.

I've corrected people on YouTube who described as "wonderful Celtic music" such songs as:

Tom Paine, performed by Pig's Ear and written by Steve Tilston ....a song about an Englishman, written by an Englishman and performed by an English band.

Who Knows Where The Time Goes, performed by Kate Rusby and written by Sandy Denny.

Dirty Old Town is often described as Irish, as are Shoals Of Herring, Fiddler's Green, Mairi's Wedding and many others whose main connection with Ireland is that they've, at one time or other, appeared in the repertoires of well-known Irish bands such as the Dubliners, Chieftains, Pogues, etc.

It seems as if any decent song or tune which is taken up by Irish performers automatically gets adopted into the "Irish Canon" and then propagates globally as an "Irish" song. Not sure there's anything we can do about it as the momentum is so great. Mostly I don't think it matters, and there are a lot of "Trad" songs that have been collected from various parts of the British Isles over time where it would be difficult to ascribe a country of origin, but in the case of your father's song, I'd say it was unequivocally Scottish.