That may be your rule, for all I know it's the USAF's rule, but it's not the British Army's, and it doesn't seem logical to me in a military context.

(I probably agree with you in the context of 'out in public and have decided you need a firearm', just not 'on a friendly military base and carrying a firearm as a matter of course rather than any acute reason'.)

The Royal Marines of 43 Commando guarding the nukes at Faslane have loaded weapons.

The Security Forces at the base in question guard strategic nuclear weapons. The other USAF command most concerned is USAFE, where the threat of terrorism against a USAF facility is greater than in the mainland US.