As fa as I see it, no gun in house, no gun accidentally in child's possession, no sister shot.
You could argue that he could have found a gun another way, but somehow I doubt that there'd be that much effort put in by the kid.
An accident happens when something can't be prevented. This could easily have been prevented if the parents had both cared enough to raise their child right and not keep the gun out in the open.
This reminds me of one of my favorite episodes of the X-Files... Clyde Bruckman's Final Repose. In this episode Mulder and Scully are presented with two psychics. The first is a murderer who sees himself killing people in the future. Rather than trying to stop himself from commiting the acts, he seeks answers as to why he is doing it. The second in Mr. Bruckman, an insurance salesman who can only see things related to death, in both the future and the past. He hates his "gift", but he is recruited by Mulder to help solve the case. The killer eventually targets Mr. Bruckman, so he is taken under protect. Eventually they meet and before he is "going to kill" Mr. Bruckman, he first must ask him why he does the things he does.
Bruckman responds, "You really don't get it, do ya kid? You do the things you do, because you're a homicidal maniac."
This kid shot his sister because he was a homicidal maniac, not because of the presence of a gun.