What I said is that no, you can't be 100% sure because too much relies upon the honesty of people (paraphrasing). Yes, a breeder CAN cheat on registration. To do so, is crazy, especially if the dogs are DNA'd, but it would be hard for them to prove it if they were not. I think that if the AKC asks, you might have to provide DNA if the dog is still living and there is a question.
I don't know this to be a fact. But, the American Kennel Club is a private organization and it can make up its own rules for its membership. You aren't protected by the government's bill of rights or anything like that. If they say, "provide DNA for this dog" then you will if you want to remain in good standing with them. Their main purpose is to record and maintain the stud books for all the breeds they recognize. So, if there is a question, and there is a way to determine the validity, in order to maintain their reputation, I think they would require DNA from a member.
Members who refuse, would probably be disciplined as though they falsified the registration, something like a 2k fine and no privileges from 2-10 years. Now this is from reading old AKC Gazettes where they list those people who required disciplinary action. Fines might be larger now, and who knows what the other penalties would be.
Losing privileges would mean, inability to register litters, go to shows, show dogs, transfer a registered dog to another owner as a registered dog, so it can be a big deal.