Bronson wrote an essay on Barbara Allen, which I'm inclined to believe. (I anticipate Malcom will tell me I'm wrong, as usual) It puts quite a different slant on the question.

According to Bronson, the earliest known version was reported by Pepys, who heard a Scots woman sing it. That would make it, not 600, but maybe 360 years old. According to his account, in the earliest version Barbara had no motivation whatsoever, including not jealousy. John, or William, or whoever, was dying, she went slowly to his bedside, he died, she saw his corpse, and laughed. She also then died.

Apparently people were not pleased, because motives creep in in later versions. She is jealous. He drank to other women. And in later versions, she becomes remorseful. But not in the original one. And apparently the original one does not say "witch," either.

But Mudcatters were not the first to worry about the motivation; that's been around from day one. I think the real mystery is in accounting for the popularity of the song.