They're wrong about that flea. It appears in (at least) some Western English forms of the song as well. (e.g. Kennedy, Folk Songs of Britain and Ireland, 226-7: The Tree on the Hill, a set from Morvah, Cornwall; with translation into Cornish).

The Bog variant turns up in East Anglia, incidentally; but in that case it seems likely to have got there from Ireland via the fishing trade, which involved a lot of song-exchanging in both directions (Harry Cox's set of Black Velvet Band, localised to Belfast and later popularised by the Dubliners, seems to be another example of that interchange).