In 2007 a womanI was overtaking moved out without looking into my lane, forcing me into a ditch. I then bounced off a tree stump in that ditch and into the path of an oncoming articulated truck. I initially thought that the owner of the truck would claim off me and then my insurers would in turn claim off the blind woman who forced me off the road for the repairs to the truck and a new car for me (it was a total write-off). However I was wrong. The truck's owners had to claim off the woman's insurers directly.
So had the woman who caused this mess not stopped, and had been unable to trace, then I would not be liable for the damage to the truck.
Also, put it this way. If you are in a traffic jam and I crash into the back of you with such force that I push you into the car in front and then do a runner, do you think it is fair that you are responsible for the damage to the car I pushed you into?