There seems to be a bit of confusion and misinformation flying around on this subject, so let me try to assist in sorting it out.
1) If the veteran's grave is UNMARKED, the VA will furnish a government headstone.If another marker is already in place, such as a civilian marker which shows as a minimum the veteran's name and dates of birth and/or death, the grave is considered marked and a government marker is not authorized.
2) If the cemetery is the type using flat memorials rather than upright markers, the government will furnish a bronze memorial plaque, but does not supply the base for the bronze -- normally of granite.This must be purchased privately.
3) The government does not pay the costs of installation of the marker.
4)The government will pay for shipping of the marker.
5)Documentation of service (copies of service records, for example) must be submitted along with VA Form 40-1330.
6) An official of the cemetery (if applicable) must sign the form indicating that the type of marker ordered is authorized for use on the grave in question. Normally, the cemetery will be consignee for the marker, which will be shipped directly there.
7) If the grave is in a family burial ground or other such private place of interment, the marker will be shipped to the person ordering it.
8) The person ordering the marker must be next-of-kin, if a relative.For example, I got my father's permission before I took care of getting a government CSA marker for my great-grandfather (my father's grandfather) because my father was officially next-of-kin as closest living descendant at the time.
Contact your local VA or state-operated veterans' cemetery, who will send you the form (VA Form 40-1330).
The above information is taken directly from the VA regulations and instructions on the subject.I hope this will clear up all the various theories.