I find "The Water is Wide" in at least 10 of my "folk" books, including the Joan Baez, Folk Song Fakebook, and Rise UP Singing. Several of them give it as an alternate title for "Waly Waly" and/or "O Waly Waly."

I don't recall doubting that any of the versions I've looked at had a "religious" origin, but I'd have to go research to see if any of them give attribution; and it does get "bent about" in some of them.

I don't think the song is really at question here, though. It's the "harmony" technique used in the performance that paddymac observed. What's needed is a music historian and/or vocal music theoretician(?) to explain it to us.

John