He was an A-6 pilot on the USS Midway in Japan. Except for the Seals and EOD guys, the Navy isn't crazy about shipboard people having personal firearms. There is very little firearms training in flight school.
I’d say your experience would have been different on a Cruiser, Destroyer or Frigate. We trained the whole crew often on everything from 50 cal MGs and smaller. We had a privately owned sniper rifle on the bridge because Surf-Pac wouldn’t give us one.