It seems like your ancestor’s military headstone should be usable to “prove” service for a Revolutionary War Society. After all, it was government issued… However, it’s not. Why?
Military headstones for Revolutionary War veterans are “derivative” sources. The marble headstones we view as the standard military headstone began to be used only in 1873. That means your ancestor’s military headstone dates no earlier than 1873, and the information on it must have been have been taken from another source.
To confirm the information, you’ll need to find an original source. The National Archives has a resource guide that can help: https://www.archives.gov/files/research/military/veterans/headstones-nonfederal-cemeteries.pdf.