Mike Yates wrote:

I actually suspect that somebody in England had picked the tune up from Sharp's collection and that was how Ray came to be using it. But, who knows...?

I strongly, strongly suspect you are (almost) right. I've drawn the clear conclusion from many years of ballad study that we don't pay enough attention to print and recordings. The number of "traditional American" songs that come from Carter Family and Vernon Dalhart recordings is astronomical. And remember that Cecil Sharp produced a number of school songbooks in the early twentieth century.

Without knowing the particular tune involved, my guess is that it was from one of Sharp's school songbooks.