Is It Wrong Not To Involve My Car Insurance?

My friends and I went on a trip to CA and rented a car. During our trip, we split ways where my friend (unauthorized driver) dropped me off to do errands while he drove around. Unfortunately, he got into an accident with another driver/vehicle. Luckily, no one was injured but the other driver (walking fine) called the police and ambulance. They filed a police report and shared my friend's insurance information with the other driver. The paramedics said he didn't require an ambulance but the other driver insisted on getting to the hospital. Our rental car was in fine condition (other driver's car was not) and we returned the car.

Now my friend's insurance is calling me stating he needs to get my car insurance involved, stating that the other driver's attorney could sue everyone involved.

To clarify, I do not have rental insurance through the rental company. My credit card does not have travel insurance. My car insurance does not cover accidents made by friends or rental vehicles. So, I doubt I have any insurances to cover for costs of damages to the other driver's car or any sort of personal injury.

My question is what should I do? Is it wrong not to involve my car insurance since I know the only result will be an insurance premium increase without any coverage of the other driver's car? I am really worried about involving my insurance under the threat of lawsuit when there might not be any claim to be had from a personal injury standpoint. Again, I would appreciate any guidance on this specific scenario