You are correct. Maybe Rico forgot to add the part where they have to tell the insurance company about the change in plates.
Certainly, you will be pulled over by the Police for driving without insurance if the number plate does not match. They will impound the car, there and then because it is uninsured.
My buddy got pulled over on the M6 because his car not on the database. When he insured the car, a couple of letters were transposed. He had to call his insurance company at the roadside to change the registration details to the correct plate before they would let him continue his journey.