Larry Bethune is speculating without, it seems, ever having looked at what Sharp did (and probably hasn't even seen the cover of one of his books, as he can't spell his name).

Look at Bronson's "The Traditional Tunes of the Child Ballads" for a comprehensive survey of how these tunes evolved. The two main points as far as Larry's concerned: very few of them are of Celtic origin, and all of them have changed a LOT over the centuries, ramifying into countless variants - tunes are nothing like as fixed as Larry thinks.