Okay, so hypothetically lets say you are leasing a 2007 Lamborghini. Nice car. Very nice. You have collision coverage on it, as is required by the lease. And some guy driving a 1972 Ford Pinto rear ends you. After all, if you rear end him, there is a good chance of an explosion! Now, you have $25,000 in damage to your car and he has a $5,000 property damage limit. What do you do?
This is an easy one. You report it to your insurance company and you let them fix your car. Why? Because if you settle with the other party, you have to sign a release. When you sign the release, you are not entitled to anything else. If the lessor decides to come back to you for "diminished value," you could be on the hook for it. If, however, you have not signed a release, you let your insurance company and the lessor fight this one out. You get to sit on the sidelines.
Remember, if you are not at fault, the smart claim is to your insurance company and let them fight to get the money back. That is not a fight you are equipped to deal with in either time or money.