Not a "claim", but a statement of fact, quoted from Planxty's sleeve notes; though whether they learned it directly from Paddy or from print or a record is not specified. Paddy himself called it 'The False Bride'.

See several past discussions here for more details; they can be found via the onsite search engine ("lyrics and knowledge search"; you'll find it at the top of every page). I doubt if there is much to say that has not already been said, but I'll just add that the verse omitted in the Planxty arrangement can be seen at Nathan Rose's website:  http://www.villasubrosa.com/Nathan/texts/tunneytext.html. Scroll down to 'The False Bride'. This is Nathan's transcription of a recording he made of Paddy; note the copyright statement at http://www.villasubrosa.com/Nathan/watson.html, and please don't copy-and-paste the text here.

"GEST" links to a completely unrelated song that he happens to have on his own website. It shares a notional title (in that form), but that is all. There are a great many songs that begin 'As I roved out', just as there are a great many stories that begin 'Once upon a time'.