Hello

With respect,

Joyce did not hear the song My Jewel My Joy. Rather, he got the papers of an Irish antiquarian who had collected one verse of it from a gentleman who said he had heard it. Joyce published the single verse.
He also published a tune which is not 'The Bard of Armagh'.

For a good account of some recent research, I suggest the Katherine Briggs Memorial lecture given y Prof R Jenkins.

His title says it all:

The Unfortunate Rake’s Progress: A Case Study of the Construction of Folklore by Collectors and Scholars
Richard Jenkins