Baldwin was handed the revolver and told it was safe. He should have checked for himself, but it's a movie set and actors may not be gun savvy.
I heard him talking and he doesn't know much about guns. A dead giveaway is when people refer to magazines as clips. The army surplus M1 carbine I hunted with as a teenager allowed one to use a clip to quickly load the magazine in the gun, and you can find clips to quickly load selected revolvers for competition shooting, but nothing made in 19th century used such clips to my knowledge. And the magazine in a revolver is usually referred to as the cylinder, not a magazine.
It is the armourer's responsibility, in my opinion, to educate the actors on how the gun works, and show them how to verify that there is no live ammunition in the gun before it is used in a scene. If you are going to be handling a real gun on set, you need to know the safety protocols for the weapon you are working with, and observe the safety protocols. Ignorance is not an excuse.