I'm pretty sure they do blame themselves. They are human. I think that when they say that maybe it was her time to go and the God wanted it this way it is their way of trying to come to terms as to why this happened, and this explanation provides comfort. It doesnt mean that they dont blame themselves.
I dont think it provides a warning to other parents if they get charged. Honestly can you imagine someone thinking "oh i was going to let my kid play with this loaded gun, but since it means i could go to jail then i wont". I think the warning to these other parents is that a child died.
Yes they were responsible for her death, the same way a parent is responsible when they leave the pool gate open and a toddler drowns, or a stair gate open and the child falls down the stairs, or they forget their baby in the car and the baby dies, or they reverse the car out of the garage and run over their toddler. I guess in all these situations you could say the parent was negligent, but it was an awful deadly mistake and as a result they have had to go through what i imagine would be the absolute worst thing to go through- losing your child. Giving them a criminal record wont help anyone, it will just make it harder for the family to carry on, find a job, look after the other kids.