Willie, it seems likely that the Manchester/Pomona version was the original, but got adapted in Cornwall to local placenames, as tends to happen. We can speculate whether that apparent local connection kept the song popular in Cornwall after it had been forgotten elsewhere. Be that as it may, it is the Cornish version which became popularised in the folk clubs through recordings by Brenda Wootton, the Yetties and the Spinners and which many people now think of as the "correct" version.

See this Wikipedia article - not always reliable but this one seems to have some convincing documentation.

As for someone claiming a song "by right", no one has a right to songs, but it is usual courtesy in singarounds and sessions not to perform something from someone else's repertoire. However if you don't know that a person sings it, or you're singing a different version, that's probably excusable. This courtesy also seems to have existed between traditional singers - singers had their "own" songs which no one else would perform.