"...which is supposed to be a transcription of the 1951 recording of Eleazar Tillett and Martha Etheridge...

Nope. Ms Pedantic here. From the book:

We find it is included in both Heart songs Dear to the American People, edited by Joe Mitchell Chapple, p. 380, as composed by W. T. Wrighton, with words by J. E. Carpenter, and in Love Songs the Whole World Sings, edited by Albert. E. Wier.

And later...

These are the words from the songster edition.

I wanted to learn this song the first time I heard it on the recording. So did quite a few other people.