Too bad that it was military records that burned. In a fair universe, the VA bureaucrats would be burned.
The veteran records that were burned were in possession of the National Personnel Records Center at St. Louis, MO. It is run by the National Archives and Records Administration, NOT the VA (and I have plenty of disrespect for the VA).
NPRC report on the fire: http://www.archives.gov/st-louis/military-personnel/fire-1973.html
see also: http://www.dd214.us/nprc_73fire.html
By the way, my own father’s records when up in the fire.