First, do I understand it that you did not have SLI or LDW through your rental channel and also declined that coverage from the rental agency? If so, it is all between you and whatever insurance you may carry. If you do have those, that is what you paid for.

Second, take the car for a damage estimate from a reputable body shop (get a recommendation at your hotel). You will likely need to pay for this, but it is well worth it. Make sure that the estimator understands that you need a "real" document which will stand up. Does not help for you to waive around an estimate of $4,000 when it really costs $6,000.

Third, read through your insurance policy documents yourself. Phone agents are trained to say "no".

Fourth, presuming that this is on you, see if you can't turn the vehicle in by prior arrangement with a manager. Nobody will give you an estimate on the spot, but it is helpful to work with someone you can then call.