That's not entirely accurate, at all. He had no more access to a weapon, than a civilian school teacher working on the base. I think civilians believe that Army & Marine Corps bases are places where weapons are just laying about. They aren't. Weapons are highly secured, at all times. If you don't have a reason to remove your weapon from the armory, you're not going to be removing a weapon from the armory.
And, there's more than a probable chance that Hasan wasn't even assigned a sidearm, unlike all other line or infantry officers that are assigned a personal sidearm. It's probably for these reasons that Hasan used his personally acquired and owned weapons.
He was an Officer, all he had to do was show up at the armory and withdraw a rifle or a pistol and say he was going to the range to practice.
Not only are officers allowed to practice their marksmanship they are encouraged to do so.