Your question is not entirely clear to me. I am uncertain if you are looking for theft coverage (pays for damage to the car you rented if it is stolen) or property damage coverage. It doesn’t make sense to go through a third party (York) for coverage you bought from Thrifty.
If you are seeking coverage from the third party because the thief was not at fault for the collision, the third party should pay. It doesn’t matter who was driving the stolen car. If it was damaged due to the fault of the third party, that insurance should reimburse the rental company. In that instance, Thrifty should be handling the issue, not you. Regardless, the theft coverage should be there to cover the damages. Thrifty can pursue reimbursement through the other party if they choose.
You should know that there’s no way for me to tell what coverage you had without seeing the rental contract. When you sign for a rental car, there are boxes requiring your initials…each of these is for a different aspect of the rental agreement that might cause trouble later. Among them are the walk-around pre-inspection, collision waiver and theft insurance.
Inspect your contract and look for the section that discusses insurance coverage. If there is no charge for theft insurance and you initialed that section, you are out of luck. If a charge shows there, you have coverage and someone made a mistake. If there is no charge, but you did not initial, you have an argument and might be able to pay the extra cost to secure the coverage.
This is an expensive claim and could get ugly. You would be wise to consult an attorney to examine the contract and accident details to find out what your rights are.