I believe most insurance companies have their policies trsnferrable. Which means that as a driver, which ever car you are driving, your insurance company will cover it.
Take for instance if you were to rent a vehicle but refused the renting company's insurance (which usually doubles the rental cost). If you were to get into an accident, your insurance company would be liable for any costs if it is your fault. You do not have to get their insurance if you do not want it.
No difference if you were driving someone else's car. The driver exclusion on most policies is to exclude drivers within your own household (like a roommate for taking it for a spin w/out permission or kids or what not).
I would check with your insurance company about their policy (or jsut read through your policy) and find out about your buddy's too. Either way, if the damage is not extensive, just pay off the damn thing so you don't have a mark on your record and possible raise in rates.