See my link to Bruce Olson's commentary a couple of posts (and nearly 3 years) ago for the best information available. Evidently the anonymous writer of the Wikipedia entry relied overmuch on misinformation posted in old Mudcat threads and outdated comment in books published a century ago rather than tackle the subject properly: the piece is a strange mixture of sensible analysis and utter nonsense.

As I've said many times before, Wikipedia is not in itself a reliable source of information and articles in it carry no particular authority. The same, of course, is true of the Mudcat (though not infrequently you'll find very good information available here, if you are able to distinguish it from the dross) - any web-based resource that allows anonymous or pseudonymous contributions and doesn't distinguish between those who know what they are talking about and those who don't will inevitably spread at least as much falsehood as truth.

Bruce was a considerable scholar, and the evidence he presents for an Irish origin of the tune seems indisputable; given the current state of knowledge, though, I'd suggest that the earliest surviving form of the words ('Pretty Peggy of Derby') can't yet be ascribed with equal certainty.