Surely, the person who loaded the gun would have noticed the live rounds?
Not if they were dummy rounds, whos purpose is to look like real rounds but otherwise lack the explodey bits.
The ones they'd use for close up scenes where an actor might be reloading, or pointing the gun towards the camera, such that you'd be able to spot that the chambers were empty. It would fit with the supposed scene that baldwin was practicing his draw, the stereotypical closeup of the fast draw threaten where the protagonist points his gun at the bad guy and makes some one-liner about making his day, but doesnt actually fire.
For example ive been binge watching ripper street recently and there are plenty of scenes where an actor checks if a revolver is loaded (a break action webley) where you see the back of the rounds or is pointing the gun toward camera and you can see "bullet" tips in the chambers.