This is sad from all sides... let's not try and place blame anywhere.
The mother states that they have no guns so it was obviously someone elses, probably a friend. A friend who probably got it from an adult in his household. The kid is 12, he's used to playing guns, cops and robbers... etc. with his friends. He probably thought he was playing another game.
I don't blame the kid for what happened or the cop for what happened. This is purely the fault of whoever owned that gun, removed the orange tip then left it around for a child to grab who then thought it was so awesome that he showed it to his friend who was then unfortunate enough to have a cop appear on the scene.
Don't go around trying to place blame on anyone involved, either the cop or the child. Both did as their natures dictated to them from training and play.
This is an unfortunate tragedy pure and simple.
I have spoken with my own kids about gun safety because I own airsoft guns and my kids uncle (on my ex-wifes side) owns real pistols. This should be the responsibility of every parent because you never know when they might encounter a gun, real or toy.