After looking at Baring-Gould's version (Child 295B) in his notebook as sung by Woodrich in 1888- it certainly doesn't appear to be a forgery.

After Woodrich text attribution, this is added, "also imperfect from Will Setter, Two Bridges, 1990." Then later when Setter's tune is given it says:

Setter sang it to the tune for "Green Bed."


Considering the tune for Woodrich's text is also given, it seems at first glance that everything is on the "up and up."

Richie