The FSNA version says, "Collected by John A. Lomax."

It's no secret that both Lomaxes (John especially) were occasionally sloppy - or creative - about texts, tunes, and sometimes even attributions. (Read, for example, G. Legman's contemporaneous review of FSNA in the Journal of American Folklore.)

Personally, I'm wary of all Lomax assertions about texts and tunes. The attribution to John may mean only that he collated this version from two or more originals. Maybe he used to sing it when Alan was a boy. Who knows?