I found an image of the 1862 sheet music cover that claims "words and music" by G.F. Root.
There was a Confederate version written during the war (as was a common practice by both sides to parody the other side's tunes) and even a pro-union one much later.
I'd say it's probably a case of careless (or nonexistent) research, considering how easy it was to find just now.
Or maybe a confusion between "trad" and "PD"? Or maybe the tune was a thin reworking of a pre-existing traditional tune?
-Glenn