After an accident has taken place, the party that becomes identified as the at-fault party must compensate the victim for his/her losses. That is why insurance companies focus on issues related to fault. The lawyers at a given insurance company undertake a thorough search for all of the potential at-fault parties.
Sometimes an insurance company might allege that its own policyholder should be charged with shared blame. If the same policyholder wanted to challenge that allegation, then he or she would need to initiate a lawsuit against the insurance company. Otherwise, the same policyholder would have to accept the reduced size of his or her compensation.