The renter is ultimately responsible for the vehicle. I suggest you reach out to the company directly and they can go over the details.
If your concerned about theft you should take their insurance even if you have your own it takes time to get payment to the rental car company and they demand payment immediately. If your in Mexico or another country you have to pay in full before they even let you out of the country. This happened recently in Mexico, long story but we had to pay in full before we could leave, thankfully we were able too.
If you're insurance covers it or you took their it might be 100% cover. If not you'll have to pay for the car
I would think you're own insurance company cover's the auto. And your rates would go up 10 fold. So good luck in reading the 49 pages of the rental agreement.
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