I'd argue their specific request regarding the V5C is not necessary and they are being pathetically vindictive and/or just demonstrating the routine incompetence these companies show.
If the V5C is a must, what happens to people who find out about a PCN years after the event where the car has since been sold/transferred/scrapped and the V5C is no longer in your possession? What happens to those who were never the RK such as lessees, hirers, courtesy cars etc.
Probs best to recite ICO guidance to them as they are clearly a bit thick. Your DL with name and matching address is more than adequate to ID you as the valid subject. The V5C has no further benefit but as above, it depends on whether you wish to be pragmatic to get the info or can wait it out.