If we put Alec Baldwin's story together we need to believe the following.
A prop gun that's actually a real gun, that was safe but had a live round in it all by itself discharged and killed a person who he wasn't pointing it at.
First he was practicing his draw but now the person told him to cock the hammer. If that's the case his cocking the hammer moved the cylinder and brought the live round to a position where it could be struck by the firing pin. He should really stop talking.