If you're certain Jesse Jones Wheeler is not the same person as the person buried under the marker, then whoever placed the marker must have confused him with the soldier in the 26th Alabama, who is Jesse Jones Wheeler. Mistakes like this happen. It's not that unusual.

Jesse Jones Wheeler, Co. "D", 26th Alabama, died October 10, 1895 in Lamar County, AL.
http://freepages.genealogy.rootsweb.ancestry.com/~fdmoore/company_d.htm

Perhaps you could could provide more information about your ancestor so we could attempt to identify him.