Agreed. This kind of mislabelling comes out of, and helps promote, a particularly nasty brand of racist cultural xenophobia in the Irish-diaspora culture. You can't hang around the Irish music for long without encountering "we created everything and the English stole it off us" - the evidence cited for that is nearly always a pack of lies.

Which came first, "Red Is the Rose," or "Loch Lomond"?

"Loch Lomond". But "Red is the Rose" is a better song. It is also an Irish pastiche of a Scottish original. And none the worse for that.

Adela Peeva's 2003 documentary Whose Is This Song? is a scary analysis of the same phenomenon in a different part of the world.