Unfortunately agreeing to pay for damage out of pocket without involving your insurance company can lead to issues like this. He does not have to agree with your offer and can attempt to get you to pay more than the actual cost of the repair.
If the scratch was the result of vandalism and not caused by another vehicle then filing a comprehensive claim should have little to no impact on your future rates. This also means that you will have to pay your comprehensive coverage deductible for the repair.
It's possible that going through the rental company for the repair will help you avoid a rate increase, but there is no guarantee that they won't notify your insurance provider. I would recommend looking into paying for the repairs yourself, but if the damage is extensive enough where you can't afford the cost then you'll have to file a claim.