This seems all about the dealer taking back the car to sell to someone else that's unaware of the car's history.
VW being reluctant to do warranty work is a separate issue.
As UK law stands, dealerships do work for which they expect reimbursement for. If the dealership fails to get confirmation that the work will be paid for by VW UK, you ultimately have to negotiate with the supplying dealer - they sold you the car, it's up to them to fix at their own cost if VW won't reimburse.
That is the position I was in with the boot lid on my Polo. VW said they weren't paying for it and referred me back to the supplying dealership 200 miles away.
Sometimes it's worth the supplying dealership to be local, even if they can't quite match DTD prices. It's amazing how many VW issues the supplying dealership end up carrying the can for.