An update with the info I received from my mom. Please note that this is what applies in Brazil to the Kennel Club (CBKC) affiliated to the FCI.

Also note that there is more than one international standard. For example, there is the FCI and the AKC (American Kennel Club) and the rules are different for each of them.

In Brazil, if you want a dog with a pedigree endorsed by the Kennel Club (CBKC), both parents need to have pedigree in order for the puppy to get one.
If you want to mate two dogs who are brother and sister, you need a special permission from the Kennel Club explaining why you want to try to fix the genes. Kennel Club might or might not allow for that. The reason is you might get lucky and fix the genes or things might go haywire and you might end up with freak shows.

Kennel Club will not issue pedigrees to any dogs with disabilities.

Also note that under CBKC rules (and I believe FCI as well) no cosmetic surgery is allowed. Not even coloring the dogs hair is allowed. If the judge picks up on any cosmetic procedure (apart, of course, to hair trimming), the dog is immediately disqualified.

I do not know who Crufts is affiliated to (if FCI or AKC). However, let us all remember that there are two sides to every story, so I add here a link to the response given by the Kennel Club in the UK.
http://www.thekennelclub.org.uk/item/2002/23/5/3