That policy probably exists to stop people from lying about their accident history. It's really hard for an insurance company to distinguish between "I didn't have car insurance in 2002" and "I had car insurance in 2002 and got into a major accident I don't want you to know about".
I would be surprised if the insurance companies had to depend on the honesty of their customers to know whether they'd be in collisions. Financial companies don't depend on my honesty to know if I've taken out a loan. They must share information about claims.