Involved in a not-at-fault accident is it your fault or the owner's for driving their uninsured car if you thought it was insured?

Ultimately, the driver is responsible for everything that that is caused by or contributed to while the driver is in the vehicle. Lights don't work? Drivers fault. Not insured? Drivers fault.  

Answer

If you drive a car that is not insured you can be ticketed for that. If you were not at fault in the accident then hopefully the other driver had insurance otherwise the damage to your friends car will have to be paid out of pocket. If that were the case then you could attempt to take the at fault driver to court. It is the responsibility of the owner of the vehicle to have the vehicle insured.

Answer

The law clearly states that it is the driver's resposibility to make sure that the vehicle he/she is driving is properly insured and there are no acceptions, you will be ticketed.