I checked the tune out in the DT, and you're right. However, two comments:
(1) I learned _Rising of the Moon_ to another, slower, more emotional, more moving minor tune which I got from Richard Dyer-Bennett.
(2) The DT's tune is recognizably similar to but different in some major details from _The Wearing of the Green_ as I have known it for many (50?) years.
In any case, thanx to everybody who has contributed to this thread and the other thread about the pronunciation of "bhuachail".
Dave Oesterreich