Amongst all the huhbub and finger pointing, the actual first rule of guns is always check that the gun is loaded.
You check the chamber and you check the ammo.
At no point should there ever be live ammo on a movie shoot. Whether that Baldwin's fault for hiring a shitty armorer, I don't know. But there where many failures up and down the line. If the assistant director was also supposed to check, they also failed.
But at the end of the line, Alec Baldwin picked up the gun and didn't or couldn't identify that the gun was loaded with live ammunition and pulled the trigger while it was pointed at someone. And that person died.