The relevant thing is whether the song praises Master McGrath as a patriotic dog, and it does. And for the purposes of the song, Lord Lurgan is presented as a supporter, worthy of a wag of the tail. Songs and stories have their own logic, and it's a mistake sometimes to let the historical facts get in the way.
My branch of the family is from Clonmel and Cahir, beachcomber. My father was a great hurler, especially in the Argentine where he went after he got out of the Free State prison in Kilkenny after the Civil War.