Bartholomew,
Doc, in the Doc Watson Songbook, says Deep River Blues was introduced to him in the late 30's by a Delmore Brothers recording.

As this was a little before John Oates time,the accreditation on the Hall and Oates album may have been due to an arrangement and adaptation. This is what doc did. The song in the book was arranged and adapted by A.D.Watson with a 1965 copyright by Stormking Music Inc.,Doc's label.