Clotheslines and kitchen knives are not designed as weapons used to injure or kill -- not a valid comparison.
I think it depends in the specifics of the case, but bottom line if a parent is negligent by allowing access to the weapon and ammo the parent should be held responsible.
What if your child was at a friends house, the friend finds the gun, with a key to the gun safe or not, accidently shoots your child. You can honestly say you wouldn't want that parent held criminally accountable? Or would you just go and shoot him?