Am I responsible for paying for another driver's rental car
Backstory: I scratched the side of an SUV while backing into a space on the street. Because the damages were too expensive and I probably would have had to pay more with a rate increase, I decide NOT to use my insurance and instead pay out-of-pocket for the damage. Now, am i 'morally' responsible to pay for his car rental?
Yes. You are the reason the other driver does not currently have a vehicle which they most likely need to get to work and maintain their obligations. If you refuse to pay for it after they have asked, they will probably contact your insurance company or the police. If they contact your insurance company, it's likely your rates would raise anyway because insurance companies see the likelihood of you filing another claim to be higher in the future. My best recommendation is to see how much it would be for a rental and keep the not-at-fault driver happy.