If a passenger in your parked car opened the door and hit another stationary car and dinged it can his auto insurance cover the damage if he is willing to make the claim with his insurance?

It depends what kind of coverage the owner has. I believe the type he would need is liability coverage (some companies may call it property damage liability), which would cover the damage to the other person's car. You may want to check how much the damage will cost. If its less than your deductable then its not worth making a claim. Even if it is a bit higher than your deductable you may want to look into how much your insurance costs will rise by making a claim. Hope this helps.