This sounds strangly familiar! I was with Privilige for ages, and when I got the 260, they tried the same one on me. I even quoted the ABI code for the car, and dug out the original certificate number of the alarm from the manufactures (as in Rover/MG). They still wanted a certificate from the manufacturer though, who obviously no longer existed. They ended up saying that I was only insured for Third Party Only (not even covered for theft therefore). I ended up telling them to do one, and went to PB.
Privilige are lacking somewhat in common sense, and basic investigative abilities, and I would knock them on the head without a further thought.