The Red River Valley is in Texas. The published version in the 1800's could possibly have been a copyrighted adaptation of the
song which could have predated that.

The problem with copyrighted versions of songs is that there is no
proof that they are the definitive originating versions.

Sam Hinton has stated that Barbara Allen was only saved as a song
in aural tradition because someone wrote it down. It was adapted
through other variants after that.

Here's the problem with folk songs. We can find an attributable
author to almost any song but there's no telling it's the first
authentic version of the song.

In some cases, there seems to be no doubt that there is an attribution before the song goes into aural transmission such as
Maud Irving's Wildwood Flower.

Remember, though, that many folksingers and songwriters put their names on traditional tunes that have been
floating around for decades such as folks like Guthrie, Dylan, and others.
Who really knows who composed these tunes originally? If you can
trace Red River Valley back to the 16th Century, you might have a point. Otherwise, it's up for grabs.

Frank Hamilton