at fault insurance company paying for my rental car?

Hi please help!

I’m in a no fault car accident and I do not have car rental coverage, however, the at fault insurance company offered a rental car to use till my car is fixed. My question is, the at fault insurance com. does not know that I do not have rental car coverage under my own car insurance policy. Can they come back and say, give us back the rental car payment because you do not have rental car coverage under your own car insurance policy after they find out?
Or these 2 issues are totally not related?

Also, is it true that if my current car insurance is paying first for my car repair and will seek for reimbursement from the at fault insurance com. later, can the at fault insurance com. still offer me a rental car to use? I live in the state of Utah.

I'm just worried that the at fault insurance com. can come after me later for the rental payment even though they agreed to pay it as of now.

The person who caused the damage is legally obligated to provide you with transportation while your car is in the shop. That is why their insurance is paying for it. They don't care whether or not you have rental coverage on YOUR policy - that would only be relevent if the accident was your fault. It is best if you let the other insurance company also pay for the repair, since they are paying for the rental, this way you also won't have to pay the deductible. It's also just easier to have one company paying for everything.

But, the other insurance company CAN certainly still pay for your rental car even if they are not paying for your repair.