Again, talking out of my ass here because I don't know the specifics of what happened on this particular set, but from what I know and have experienced so far in my career, I think this accident happened because there was a failure somewhere in the chain of custody of the Dummy rounds... from the time they were made by a prop house (more than likely by an experienced armorer) and traveled to set, and into the prop gun.
Again, this is going to fall onto the armorer, and the 1st AD. Clearly, normal and longstanding established protocol was violated, resulting in this tragic accident. Whomever brought live rounds to set will bear responsibility, along with the armorer and the 1st AD. But in all likelihood, it was the armorer herself that mixed up live ammo with the dummy rounds.
The stories of crew plinking with the prop guns (or their own personal firearms) are absolutely mind-boggling to me, for many reasons. I have a hard time believing that went down in any way, but if it's true, it's another colossal failure by the armorer and the producers to let that happen anywhere near set. This story will probably turn out to be bullshit driven by the media - but if not, it's mind blowing.
I have another scenario to propose all of the people that are saying Alec is solely at fault since he pulled the trigger. Imagine for a moment that you have a kid. A young kid, say 11 years old. Say you're at the range with your kid, and you want to teach them safe firearm handling, and you let them fire a pistol downrange. What happens if your kid discharges that pistol and somehow kills someone? Does your kid go down for Murder, or Manslaughter? Or do you as the parent? Or perhaps the RSO? That's the way this will play out in the investigation, because film sets are not the same as the real world when it comes to this type of thing - the responsibility falls on the professional firearms expert, aka the armorer - whom in this case would be the Parent and the RSO all rolled into one. Even though he is an adult, similar logic to him being a child will apply. As an experienced actor, I'm positive he would have been operating under the assumption that there would never be actual live cartidges anywhere near set, let alone loaded into the revolver he was handed. Again, the typical rules of gun safety go out the window on a film set - because for the most part, they can't be adhered to.
Also, as an aside, there are usually law enforcement officers present on film sets when production is happening on location (actual police / sherriffs / highway patrol) and whenever simulated gunfire is going on outside of a stage. They act as security for the set, maintain traffic barricades / road closures, as well as letting the average person who happens upon a location shoot and hears gunfire that everything is on the up and up. This is typically mandatory per the permits granting permission for film production to happen (but maybe not in NM?).