All insurance agencies report everything to the DMV. That's why it's not a big deal if you get caught having forgotten your proof of insurance (unless the cop doesn't like the way you look and wants to make your life hard). Otherwise, the cop can just go look it up on the computer.
_Additionally DMV doesn’t require insurance on mopeds reading information of web page now._
What does this mean? The Motorcycle Handbook says, "the financial responsibility sections of the Vehicle Code apply to all two-wheel vehicle owners and operators." It seems pretty simple to me. Get insurance or otherwise be able to show financial responsibility and comply with CVC Division 7.
PS: Awesome pictures on that announcement. Motorized scooters, motor-driven cycles, and motorcycles all have nice factory showroom white background photos, but the moped is just a picture of some TFR in a parking lot stolen from mopeds.com.