Is your argument based on "temporary substitute vehicle" clause

First, the outcome depends on the state of the auto insurance and its laws. There are in some states has cases allowing policy covering unauthorized driver of temporary substiute vehicle. See http://www.insurancejournal.com/news/southeast/2011/11/28/225266.htm

Second, however usually temporary substitute vehicle (covered by the policy) are defined as a car rented when the insured vehicle was in repairs. It does not include cars rented on vacation. Otherwise why would American Express advertise "rental car coverage"?

Third, even if the rental car is considered temporary substitute vehicle, you have to also assume LZ's has comprehensive/collision coverage on his own policy. Merely liability insurance won't cover damage to his own car.

We are dealing with philosophical debates that might have nothing to do with LZ's case.