Natural selection doesn't occur amongst pet dogs because there are owners to prevent matings occurring, to take dogs with genetic conditions to the vet and make decisions about whether dogs should have treatment or be pts etc. That isn't random genetics at work; even if the two dogs mated accidentally, someone has still decided a) to allow that to happen b) knowing that it did happen, allowed it to continue and c) decided what to do about the puppies [and I think you are doing the right thing re-homing yours via the DT, btw].
I'm not a veterinary scientist so I can't write you an academic paper, but let's talk about hip dysplasia since it's such a common problem. It's an awful inherited condition that certain dogs are prone to, such as german shepherds and labrador retrievers; the dogs go through a lot of pain before being pts. Responsible breeders wait until their dogs/bitches are old enough to have X-rays to look at their hips and see if they are likely to have problems or not. If they are, then they don't breed from those dogs. That's why, in the thread about getting a dog that DBF started, it suggests asking a breeder for the hip scores of the parent dogs. That way, you can know that HD is unlikely to be a problem.
Suppose you had a labrador retriever, and you hadn't had it hip scored, but you decided to let it mate with the dog next door which happens to be a german shepherd, but also hasn't been hip scored. The resultant dog would not be a pedigree, but it is still possible for it to inherit HD from both parent dogs.
So, you wanted references. For example, Swenson et al (1997) in the J.Am.Vet.Assoc., looked at HD in german shepherds and found that after 5 generations of selective breeding, incidence of HD decreased from 55pc to 24pc.
Now if you only considered HD in breeding and nothing else, you might end up with an in-bred population and lower genetic diversity. But apparently you can also get in-breeding scores for dogs which means that you can try to decrease HD and get more diversity at the same time. See Zhang et al (2009) Am.J.Vet.Research which looks at the genetics of HD in several breeds of dogs.
Like I said above, I'm not a veterinary scientist or dog breeder, so there will be others out there with a better understanding of the field, but that at least answers your question.
I don't think there is anyone on this thread who doesn't think there is a lot wrong with the way dogs are bred at the moment. But the existence of pedigrees isn't itself the problem, and nor would anyone want to wave a magic wand and send all the dogs out to survive on their own in the wilderness for a few generations to sort out the problems.