Who ultimately decides who is responsible for a car accident?

I am in Florida, we are a “no fault state,” I do not know how it is different in CA. However, if the insurance company assumes no responsibility, then your insurance should be easy to pay for your repairs and other damage. If your insurance company really feels like the other drivers fault, they are gone and will try to recover the money. If your insurance company files the claim as a “burden” when it appears on the record as an accident at the fault location.