Am I liable for loss of use charges and administrative fees for a damage to a rental car if I opted for my own insurance coverage?

Question Details:

I rented a car 4 months ago. The weather the next day involved heavy rain and I hydroplaned on the highway, damaging the car severely. I opted for my own car insurance coverage during the rental process. My company has paid for the damages, less my deductible, and considers the claim closed. The car rental company is trying to collect "loss of use" charges for the time the car was unable to be rented out, as well as some sort of administrative fee, as they had to process their own claim. I signed to this in the rental agreement, apparently. Is this legal in WV? Do they need to prove it?

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