I will 争一争，If I have 理

However, from what the OP posted, I am not sure if he (or she - we dont know) has 理 or not.

My wild guess is, they might not, and already paid the rental car company. (judging by the fact they did not keep the contract - if you have good 理, wouldn't you safeguard the contract and fight to the end ?) However, now they may realize their car insurance may cover the damage minor deductibles - but it requires the rental car contract to prove the insurance holder also listed as additional driver on the contract which they threw away (lost). So they asked here.

Unless the person come back to give all the details, nobody would know. It is only my wild guess.