Ok, everyone's entitled to their opinion, so mine is diametrically opposed to some expressed here.I'm with Tootler and Leadfingers!
For me, the tune works best as a slow air/lament: the slower the better, and please, OMG NO NO oom-ching-ching of accordion basses turning it into a waltz. The C chord (yes C) is just fine too. Yes, wallow shamelessly, and enjoy it!!
And has the person who wants it in strict tempo never heard of rubato? It can even work in a session, provided the other musicians are actually listening to the leading player, and not just getting their heads down and taking off at their own pace.
The recording that really hit the high spots with Classic FM (and where I first heard the tune some years ago, before it got so popular on the folk scene) was with Major J R Perkins conducting the Band of the Royal Marines: I think it was this version that was used as the theme music to The American Civil War" TV series. This, and the version played by Aly Bain and Jay Ungar himself on the first series of Transatlantic sessions are the definitives performances IMHO.
See aso a long thread started in 1998!