State laws can differ but usually if your car is stolen, thus used without your permission by the thief, you are able to put in a claim through your comprehensive insurance coverage. In this situation you are typically not held liable for damages caused by your vehicle to other people's property while it was in the possession of the thief.

It would appear that there may be extenuating circumstances regarding your stolen car claim since it was denied and instead your insurer wants the claim to processed as a collision claim. Due to this you will want to ask your claims adjuster if you will be held responsible for the claims of the owners of the parked cars. If your insurance carrier is accepting the claims of the owners of the parked cars you will need to find out from your insurance company why this is.