Thank you for the information and your question. A basic tenet of automobile insurance policy
law, which is in your policy/contract
language, is that unless the insurance carrier can establish liability by actually speaking to the other party and/or seeing their vehicle or obtaining a police report with all the details contained therein about the drivers and the accidents, they are bound to pay out anything for the accident. That is why it is so important, and actually required by law, that drivers exchange complete information regarding insurance and names, etc., at the time of the accident.
So, unless you have something that can help your insurance company locate this driver, for example a license plate number, insurance policy, name,etc., they can lawfully deny your claim.
You have the right to file a complaint with the Arizona Insurance Commissioner, and they will follow up with the insurance company, but the resolution will likely be the same.