Completely false. All the return shows is "insurance information on file" for insured and "insurance status not checked". Law enforcement officers do not have access (on a DMV return) to what insurance company or policy number drivers have.
The DMV has electronic communications with insurance companies and when a policy is cancelled, the DMV is notified of the cancellation. The DMV will usually wait for a short period of time to see if another insurance company picks up coverage for the VIN number, which most of the time happens. After a prescribed time of no validated coverage, the DMV sends out a letter to the registered and legal owners of their awareness of the cancellation of coverage for the vehicle. They ask in that letter to please provide the nee insurance information. If you provide the new insurance, no big deal, the problem goes away. If not, the DMV will suspend the vehicles registration, which the driver or registered owner can now be subject to citation.
An NCIB check usually would show an insurance company and policy but those checks are outside the scope an officer investigating a traffic accident.
Once again, the officer on scene has no idea who the insurance company is. That is why you are required to show proof of insurance at the scene of an accident.

