The tune Andy Irvine accidentally set to Willie of Winsbury actually belongs to Fause Foodrage. It's on the previous page from a genuine Winsbury tune in the tunes appendix of Child's English and Scottish Popular Ballads; presumably Andy didn't notice that the page had flipped over when he went to copy it down. It's easily done.

There is no evidence that the Foodrage tune was ever used for Winsbury prior to that. If Barbara used that tune, then it came from Andy originally, at whatever remove.