That's precisely why I steer clear of Scottish songs, Ross. I can't do the accent, and Scottish dialect sounds ludicrous in an English accent, and worse in a bad fake-Scottish accent!

I do think there's value in some of the comments others have made above - that accents are absorbed by performers by a sort of process of auditory osmosis, and it could possibly be that some don't detect the difference between the American accent and the Irish one, and think they're singing in the latter when they're actually using the former.

Why it should be that unaccomperated singers don't lapse into mid-Atlantic (according to GSS, although I've never become aware of that myself), I'm really not sure, unless it's because they have less to think about that a singer who plays an instrument concomitantly.