Yes if the assumption is that the driver at fault was the car driver but what if the motorcycle was the one at fault? This happened to a friend of mine. My friend was moving forward when a speeding motorcycle beat the red light and rammed straight into my friend's car. The motorcycle driver broke his leg pretty badly as he tried to swerve but lost control. My friend's car was damaged. A policeman was there and said that it was the motorcycle at fault but they had to rush him to the hospital because of his broken leg. My friend didn't bother to go after the motorcycle driver anymore as he didn't look like he could pay for my friend's damaged car.
I agree though that if it is the car driver at fault, the car driver should pay for the injury.