Legal Question in Personal Injury in Ohio

You are almost certainly responsible for the damage. I'm reasonably sure the rental agreement says so. Additionally, when you declined to pay for the additional insurance the agent would have explained that you were accepting liability for any damage to the car.

Whether the company has insurance is irrelevant. Assuming that an insurance company paid for the damage, it would then be able to bring a subrogation lawsuit against you to recover what it paid. (Many people believe that insurance companies must absorb the costs when they pay claims, but that is not true. They are generally free to pursue a third party if that party is legally responsible for the underlying loss. Insurers usually bring such lawsuits when it seems cost-effective to do so.)

I'm sorry I can't be more encouraging.

I should add that, if someone else is at fault for the accident, you probably have the right to seek reimbursement from her. If she is insured, her insurance may cover some or all of the amount you have to pay the rental car company.

Note that the company's right to reimbursement from you is independent of your right to reimbursement from a third party. It does not have to wait to see how your dispute with someone else is resolved, and it is entitled to recover from you regardless of whether you obtain relief against anyone else.