The fire happened in 1973. Millions of records were destroyed and were not recoverable. I suspect his records were among them. In most cases where a military record has been presumed destroyed, NPRC is able to reconstruct basic service information, such as military date of entry, date of discharge, character of service, and final rank. Other than contacting the NPRC I don't know what you can do to prove his service.
National Personnel Records Center fire - Wikipedia