According to Wikia for FOV the armory is unlocked in the Overseers office. Unfortunately when I looked there was no such option. How do I get the Security Vault door open. (Playing on the PC.)

From the Spoilers forums....good luck.

http://www.gamesas.com/index.php?/topic/1161153-i-need-help-retrieving-the-all-american-from-vault-34/

http://www.gamesas.com/index.php?/topic/1168247-vault-34/