It's too bad that Baldwin lied(why???), that's no doubt a huge 'red flag' for investigators. IMO whoever made the decision to use live ammunition on the movie shoot has to bear *some* measure of responsibility.
What was reported earlier is more likely. During breaks in filming, they were having fun plinking at tin cans in back of the set. The gun was not checked for live ammo remaining before rehearsing/filming.
Another possibility: For realism, blanks are sometimes made to look the same as live ammo & that could have caused confusion.
When I worked in retail firearms & instruction, I saw a similar issue that resulted in an accidental discharge in the shop. Luckily, an important rule was followed (point in a safe direction), so the result was not tragic - just a hole in the wall.
I saw some live ammo in a drawer, mixed with dummy rounds. Dummy rounds are cartridges that are missing a powder charge & a live primer, so they can't fire, but otherwise look exactly the same as a live round. The purpose of dummy rounds is to instruct new gun owners on loading/unloading/checking procedures. I suggested to my co-workers that they should not have live rounds & dummy rounds in the same place. They didn't listen & said I was being "Paranoid."
Later, while showing a customer the loading/unloading procedure, an employee pulled the trigger to demonstrate that a dummy round wouldn't fire &....the gun fired.
There are safe dummy rounds that don't look like regular live ammo; they are made of plastic or aluminum & are brightly colored to avoid such issues:
When I taught, I always used these. They come in all calibers & are easily recognizable.