"Jim, is that Cunningham was a noted fraudster regarding supplying old ballads"
Am aware of that Jim - have a copy of Cromek's "Remains of Nithsdale and Galloway Song".
While he was making claims regarding his own work I think it highly unlikely that he would either dare (or even bother) to make claims regarding somebody else's, certainly not to the extent of naming their sources.
The couple of verses he gives are well known enough not to be fakes.
Jim Carroll