"Kids break bones occasionally. Why must everything be someone's fault?.....
This is why you have health insurance."
It can turn into being someone else's fault b/c of the forms that many insurance companies send after accidents. They ask who else might be at fault. If you put someone down, the insurance company is going to go after that person.
So insurance companies do not like paying out when someone else is at fault, which is why they send out forms asking who might else be responsible for the problem.
Okay, first the examples you show are property related and yes, auto and homeowners/renters insurance companies want to know what happened and who did it because it's obvious in those circumstances that someone was driving the car. Property damage is not treated the same as health claims unless the health insurance claim comes from something like a car accident that has it's own claim. Your examples have absolutely nothing to do with a child breaking a finger. Obviously someone did something that they are liable for. Health insurance companies do not ask for who is responsible when a child breaks a finger.