You could very well be right, Philippa; I tend to take the sceptical viewpoint simply because so many people believe what they want to, regardless of the evidence (or lack of it).   I guess that what we need here is a melody that is clearly related to both the Scandinavian and Scots/English groups; it would certainly prove your point.  Bronson was of the opinion that tunes changed less fundamentally, and at a much slower pace, than words, so a clear relationship might be demonstrated that way.  As you say, the Gaelic song is obviously quite separate.

Malcolm