No, the AD didn't take the gun from the armorer - he picked it up, declared it cold himself, and handed it to Baldwin. None of which he was supposed to do in his capacity as AD. That's how he was negligent.

The armorer wasn't present at the time - she was on set somewhere, but not told they were about to use a weapon as it was an unscheduled rehearsal. The AD decided to proceed without the necessary supervision.

And the armorer wasn't even working as armorer at the time - she was hired for two jobs: armorer and props assistant, and days before the shooting a line producer had told her off for dedicating too much time to weapons safety and not enough to assisting the props master. She pushed back, complaining about the lax gun safety on set, but was overruled. So on the day of the shooting she was elsewhere, assisting the props master, as she'd been told to.

The whole thing is a clusterfuck of bad management and complacency, but at the end of the day the AD should have known better than to use a weapon in a scene that had not been checked by the professional person whose responsibility it was to check it.