On reflection, I don't think the sequence of events I just suggested is plausible. The Caledonian Pocket Companion was fairly influential, but not so influential that it could have driven the adoption of a new tune for "Barbara Allen" across the entire English-speaking world.

This may be what Maclean had in mind:

The Old Woman of Glen Lyon

Anybody know a Gaelic song about it? Does it still go to a tune like "Barbara Allen"?