Richard, you are right about the tune. There are three tunes in circulation which have been borrowed, changed, and interchanged. They are:

Ned of the Hill
Lambs on the green hills
Niel Gow's Lament for his Second Wife

I have been working with the tune for Ned of the Hill from O'Neill's. The poor thing has been fiddlefied to within an inch of its life. It's got dots, it's got swoops, it's got sixteenth notes, it's got runs up and down the scale where we forgot how it goes, and it's got a range of an octave plus a fifth. If ever a woman's voice sang of a desirable young man named Ned, that voice has been swept up and tossed out.

And when I got done with all my work on the tune in O'Neill's, I had a pretty good melody, but one which you can hardly put any chords to. So if you have a folk act, what are your accompanists supposed to do? Better just to borrow some other tune, say Niel Gow's 'Lament.'