What is the nature of the accident anyway ? Is there Police involved ? Did it involve other car ? Your fault or other's fault ? The driver does not have car insurance ?
You need to tell the truth, and no tricky lie. That is my advice.
Remember once you claim against your own car insurance, your premium rate will go up (sometimes A LOT and stay high for a few years) when it comes to renewal time. Some insurance companies, such as Farmers, may drop you (non-renewal). So you have to weigh on the Pro and Con to decide if you want to file claim with your insurance, especially if it is your own fault.
OK, I guess you can call :
1) Hertz corporate office to ask them for a copy of the contract - even if the local office claimed they shredded the paper one, they should have computer record to show you are the additional driver - many times additional driver also involved additional daily fee - the contract should show that charge. If what you told is the truth, then the computer print out should show you as additional driver.
2) If you cannot get your rental contract copy this way, call AG office (Attorney General) in Alaska State - ask for Consumer Protection or similar dept - explain your case, give them the details. They should be able to help you or at least advise you how to deal with it.
I sure hope Old Goat read these so he would understand better the whole scheme of things. I KNEW this is the case judging from what you asked. There is not a matter of "I just like to fight with Americans". You need to know how to work with the system.