This page says John McDermott was born in Scotland in 1955 and raised in Canada, and has been a member of the "Irish Tenors" group. John McCormack was born in 1884 and died in 1945, so the McCormack recording should be at least ten years older than McDermott (unless there was another John McDermott).
So, until I receive proof to the contrary, I'm going to go with the Frederick O'Connor attribution.
I found a very nice recording of the song by John McDermott - he uses almost exactly the same lyrics as the McCormack recording.

I still question the line "sailed their wee boats on the burn." It sounds like "burn" on the McDermott recording, but more like "Borne" on the McCormack recording - or could it be "berm"?

-Joe-