1. The song refers to the Shenandoah River, of which only a small fraction flows thru (sic) WV, the rest of it is in Virginia
2. Also referenced is the Blue Ridge Mountains, virtually none of which are in West Virginia
3. Rumor has it the song was originally entitled "Old Virginia"
#3 explains the confusion created by #1 and #2. I first learned of this from Joab Corey, who learned this from his High School Civics Teacher. Like many songs, the inspiration has a lot of folklore to it, so it is unclear, but very amusing.