By his description, it sounds like a case where the multiple layers of people being responsible for checking had the opposite of their intended effect. Each person in the chain assumed the previous person had performed the proper check, and skipped doing it themselves. This post says the armorer should be the one who hands out weapons, but I have heard elsewhere that the armorer is supposed to hand them to the AD, who is supposed to perform his own double check. But having one person solely responsible for checking and handing out the weapons would avoid this mistake of someone thinking someone else already did the work.
This post thinks the armorer was playing with the guns on break, left them on a cart still loaded, walked away, and then the AD grabbed them, thinking they were loaded with blanks. That seems to be contradicted by reporting elsewhere in this thread though, which says the gun was inspected after the shooting and was found to have dummy rounds in it.
I agree with your assessment of the accident chain ... I don’t know enough about this to compare the various accounts of the procedures on set, but it does seem clear that the safety checks we do with our firearms, or a friend’s, is not the same procedure on set.
It’s obvious that several links in the safety chain were ignored and/or outright broken.