
There are many that claim Accredited status that are not, have you confirmed with the kennel club that they are or were KCAB.
Some of these puppy producers are misleading people in the same way as with registration advertise registered pups when they are not 'Kennel club registered' the same with Accredited breeder, they are not Kennel club Accredited but some mickey mouse outfit or simply a registered commercial breeder with their Local Authority.
The kennel club when provided with proof of breaching conditions of the scheme remove KCAB all the time, though they do have to check allegations in case they are malicious.
If you are suggesting parentage DNA verification for every puppy registered with the KC this will add an awful lot to the already high costs of breeding properly, already you have the general public happily going to puppy producers for a cheaper puppy as they see no need for even the basics fo KC registration.
Just the practicalities of testing a litter of puppies correctly (they need to be segregated from each other, be fully weaned to ensure an uncontaminated DNA sample, and then there would be a long wait for the results (labs would be overrun with applications delaying homing of puppies.
I for one would not be able to segregate a litter from it's dam to be sure they no longer fed from her, or from each other for half a day as in 'my home' I do not have half a dozen or more places to put individual pups, nor would I want or need to.
Most people that we call breeders use outside stud dogs (so two people would need to be falsifying records), they have no need to pretend wrong parentage as it has no purpose, the parents are the parents, and in a lot of cases one can tell just by looking who the parents of a dog are.
On the other hand I would be more than happy if 'commercial ' kennels (those required to be licensed by the Local Authority) had to do this, breeding from their 'anonymous' bitches and stud dogs, as it would add to their costs.