Family oral traditions about an ancestor's Civil War service are notoriously unreliable; however, yours has a ring of truth to it -- it's straightforward and unembellished, and it fits with what is known about Fristoe's regiment.

No muster rolls of Fristoe's Regiment Missouri Cavalry exist, so far as I know. The Compiled Service Records consist only of Federal prisoner of war and surrender and parole records. These are supplemented by a small number of postwar Confederate pension records. As a result, the only proof that a man served in Fristoe's regiment depends on whether he was captured at some point, or surrendered at the end of the war, or applied for a pension. A man who was killed in action would have no record of service. Company G was recruited mostly in Oregon County, Missouri. Since John A. Simpson's brother served in this company, it's likely that he did, too. Since he was killed before the end of the war, however, there's no record of him.

I know this doesn't help much, but it explains why you can't find John Anderson Simpson among the records of any Missouri regiment.