So, assuming Baldwin is telling the truth(and you'd be a fool to assume he is not covering his butt and lying at least at some point), this is how the scenario plays out in my mind:
Alec Baldwin is holding the gun for a shot. The cinematographer has him cock a SAA pistol for a test shot in the camera. They're testing how well it comes through on the camera, with him thumbing the hammer back. At this point, it's probably past half cock, into full cock, as they are paying attention to the angle of the shot.
Baldwin releases the hammer after they get what they want for the shot. The hammer goes forward, gun goes off.
Baldwin thinks there's something broken on the gun, and the hammer is broken and goes forward on it's own, without staying locked back, and that he never touched the hammer.
What I think happened: Both Baldwin and the cinematographer were paying attention to the angle of the gun and hammer for getting the right shot for the camera. They were both focused on it, and Baldwin didn't realize he was thumbing back the hammer while pulling the trigger. Releases the hammer when they get the shot, and the gun goes off. Negligent discharge, but sorta not really but kinda understandable for a non gun guy trying to work out a lighting and camera angle scene to make. Which leads back to why the gun would be loaded, even with blanks, for that.
That's assuming we believe him. I would bet, since this was for a movie, this was all recorded, so is probably decently close to what happened.