I've had one accident with a rental car - I got rear ended while stopped at a red light in MSP. The police never asked for proof of insurance - not sure if they asked me for anything. They wrote a report and listed the other driver as at fault, even though she did not get a ticket. I picked up a copy of the police report the next day and gave it to the rental company (Enterprise I think) with their own accident report form. Where their form asked for insurance, I listed my company name as it was a business trip and I did not want to involve my insurance unless absoultly necessary.

I got a letter from Enterprise a month or so later saying they were going after the insurance company of the girl that hit me. Never heard anything about it after that.