The ballad "Johnie Armstrong, Child no. 169, has nothing to do with "Parting Glass."
Bronson, "The Singing Tradition of Child's Popular Ballads," says the first record of a tune was called "Good night and God be with you." What this was, we don't know. "An earlier tune "Ihonne Ermistrangis dance," mentioned in The Complaynt of Scotland, 1549," (Bronson) is unknown now. Present tunes are all 19th c. Scottish.
I think your author (Tuchman? sp.) was just telling a good story, putting two and two together and getting eleven.

Malcolm Douglas would have the best information; pm him.