While it may seem like tombstones are public things that should be free for photographing, that may not always be the case.
Apparently, in some cemeteries, photography is not permitted. It's not an issue so much of the photographs themselves, but of what you're allowed to do on private property...
Cemetery photos: permission required?
the standard suggestion for photography in any cemetery is good advice regardless: get the rules of the road in advance know if you need permission, whether theres a fee, and what the hours are so you dont accidentally get locked inside the gates.via: www.legalgenealogist.com
So what this comes down to is not ownership of the images of tombstones, but the photography activity on private property.
A museum may prohibit photography of artwork that they don't actually own the rights to.
The artist may own the copyrights of that image.
A live performance venue may prohibit video recording of performances.
The band owns the copyright of the performance itself.
I wonder if, from a legal standpoint, there is ever copyright ownership of the actual tombstone image itself? Is it a work of art?