A little bit of web-looking doesn't turn up the TV show "Shenandoah". Not even 40, my TV memories [while jam packed] don't go back that far. Nonetheless I am sure this Shenandoah TV show existed.
I so like this suggestion, it is very likely, and points to a place where this "western" song that is in no real way western became western.
The Hollywood connection.
I could drop it all right now and feel the answer has been found in good ole Hollywood. Still, one has to wonder why Hollywood of the 50's thought Shenandoah so emblematic of the West. Copyrights and royalties not withstanding, pub domain songs have their attractions, but why this song for a typical western. The name of the dang show came from the song as well, it seems, begging the question.
Mor's good work just brings the point more painfully into focus: Why is "Shenandoah" considered a theme of Western Expansion?