I was traveling through the lane of a parking lot at a service station and was not backing up from a parking space, but going forward when another vehicle pulls into a parking space and then rapidly backs out and strikes my vehicle on the rear quartet panel. She stroke me so hard that it flattened my tire and bent my rim. I called the police and they did respond, but took no action because we were on private property. My insurance company tells me that I should take the vehicle anywhere I want to get it repaired, but will need to pay $250 deductible. I believe I am not the responsible party as I believe the other vehicle is 100% responsible. This happened in Tennessee. I don't believe I should have to pay a thing, plus I will now need a rental car. Who should pay...

If you were driving the correct direction in a driving lane and a person backed out of a spot and hit the rear of your car (which is what you say) I see the other person totally responsible. I am surprised that your company isn't going to pursue the other party for your deductible. That is the usual procedure.

As far as the rental car, do you have rental car insurance?

If not, your insurance company might attempt to collect on your behalf for the deductible but you will have to sue in Small Claims Court for the rental car... and the deductible portion if that is the route you choose to take.