Reminds me of what happened on one of my projects a couple months ago...
A coworker was driving a rental car rented by another coworker, which is allowed under our Hertz CDP. However, I guess they draw the line at getting pulled over for speeding 25 miles over the limit. In this case, even though the driver was allowed to be driving the car, Hertz instructed the state trooper to have it towed. Extreme? Yes, however I can't imagine what they would have done had he gotten in an accident.
For business purposes, I rely on the fact that our rental agreement lets us drive cars rented by others. For personal use, I err on the side of caution and purchase the AMEX Premium Rental Car insurance (about $15-20 per rental, not day). Sure, my personal car insurance covers me, but I live in NJ, am male, and relatively young. If I did get into an accident, I'd prefer to file with AMEX rather than my own insurance and face a premium increase. Back when I was 17 I had one year where my insurance was $7000 (yes, seven thousand). It was partially my fault and partially due to being in a high insurance state, however I don't want to venture anywhere near that high of insurance ever again.