The story in the song may or may not be true, but it may well contain some historical references. Three extracts from Wikipedia;

1. The song appears to have originated with Canadian and American voyageurs or fur traders traveling down the Missouri River in canoes, and has developed several different sets of lyrics.

A version of the song called "Shanadore" was mentioned in Capt. Robert Chamblet Adams' article "Sailors' Songs" in the April 1876 issue of The New Dominion Monthly.

Lyrics from prior to 1860, as given in Sea Songs and Shanties collected by W.B. Whall, Master Mariner (1910), were reported as follows:

Missouri, she's a mighty river.
Away you rolling river.
The redskins' camp, lies on its borders.
Ah-ha, I'm bound away, 'Cross the wide Missouri.

The white man loved the Indian maiden,
Away you rolling river.
With notions his canoe was laden.
Ah-ha, I'm bound away, 'Cross the wide Missouri.

"O, Shenandoah, I love your daughter,
Away you rolling river.
I'll take her 'cross yon rolling water."
Ah-ha, I'm bound away, 'Cross the wide Missouri.

2. John Skenandoa c. 1706 – March 11, 1816), also called Shenandoah, was an elected chief of the Oneida.

A longtime friend of the minister Samuel Kirkland, a founder of Hamilton College, his request to be buried next to Kirkland was granted.

3. Shenandoah Valley; Various accounts tell the origin of the name. According to one, General George Washington named the valley (and river) in honor of Skenandoa (or Shenandoah).

However, the name was in use when Washington was a child, as evidenced in land grants and correspondence.

It is also said to be named after the Senedo people, a little-documented tribe said to have lived on the north fork of the river and destroyed by the Catawba, some time between 1650 and 1700.