The last time I got a rental car from the Toyota dealer (because I didn't want to wait in the waiting room). I had to provide my driver's license and insurance certificate at the time of rental. The contract I signed was similar to Tesla's so I really don't see the problem here. If you rent or drive someone else's car you're responsible for any damage that happens (whether you sign something or not). Signing the papers is mostly to remind you that it's not your car.