A pistol like the one he uses has single and double action capability. Whether the hammer was cocked, or not, the ONLY way that gun fires is if you squeeze the trigger. It might have been a feather light trigger, but even then, I doubt it as there is always a draw up on EVERY SINGLE TRIGGER. So Alex Baldwin is a fucking liar.
Most of the look alike guns are both single and double. If it is just a single action then, he had to have cocked it and squeezed the trigger. A gun that is cocked like that if all it took was movement to make it go off, would have gone off while he walked or put his hand on it.