Insurance companies do not adjudicate fault. Do you have the police report yet? That will go a long way in determining fault. And under no circumstances, even if your insurance company accepts the liability, should you admit fault.
Actually, they do. As a former adjuster, it was up to me to determine which driver was at fault, then pay/deny accordingly. Police reports can be very helpful, but they were not the be all/end all when making my decision.