Gravestones can be false 'witness' --may be placed where person not buried --may have wrong birth and/or death dates
Family associations may put up gravestones with narratives that relate what they believe but have no first-hand or fact-based knowledge of.This has happened often, say on 100th or 150th anniversary of the deceased person's death.
One very distant cousin instigated having a DAR marker placed on the old gravestone of one of my ancestors (he d. in 1819) in 1964.There is no evidence that he served in the Revolutionary War, although the same name is on one surviving militia list (which was a roster with no indication of active duty service anyway).
If you have not done so, you would need to look at the gravestone and evaluate when it was created.Close to date of death would have more credibility than decades later, but still would be only a clue awaiting evidence.
No few men told stories that were not strictly true, including applicants for pensions under supposed Revolutionary War service.Stories can misunderstood by listeners, and/or embroidered when retold.