From what you explained, I can't see how anyone would liable except the driver of the vehicle that hit the car. We are all responsible for our actions, regardless of what may have "driven us" to an action.

If the owner of the vehicle you are driving has insurance and they gave you permission to drive the vehicle, then the insurance on that vehicle should pay the claim - unless their policy includes exclusions against certain driving classes (i.e. no one under 25 is covered under this policy, etc.)

In addition, the vehicle you hit can file the claim under their policy and the company (or your friend) can try to seek the damages from you (or at least their deductible) IF they have physical damage coverage.