On the basis of my reading so far:

Harker's central topic isn't which songs are and are not folk songs, it's as much or more about the historical narratives that the mediators told about these songs and about the subjectivities and cultural attitudes and activities of people in the past. For example Lloyd's book on folk song in England.

So one thing he criticises about Lloyd is his assumption that he knows what people in the olden days would have been thinking and feeling, about what Harker calls their 'psychology'. He gives examples of statements about such things that he finds lacking in evidence. I think this is probably a fair point.