As a member of the BCOA Native Stock Committee and the person assigned to looking into the exsistence of DNA testing for proof of breed identity, I will say that at this time there is no DNA test in existence that can prove a dog is purebred. The current technology can tell if a dog shares markers in common with different known breeds of dogs but can not tell if that dog is purebred. The technology is just not there at this point in time.
Next, in the basenji breed there are currently only 2 hereditary disorders that have a DNA based test, those are Pyruvate Kinase Deficiency referred to as both PKD and HA, and Fanconi Syndrome. All other known inherited diseases in basenjis have health tests that should be done to determine the status of the parents but do not tell you the genetic make up of the dog. The best guidelines for breeders are published on the OFA website and have been shown to work very well when employed by breeders to decrease the incidence of genetic disease where no DNA test is available. These methods require both depth and breadth of health testing in the pedigree to make educated choices.
Honestly, I see no good reason for AKC to open their stud books up to dogs born in the US of US born parents that are "purebred" basenjis but are not of AKC registered parents. These dogs are not AKC registered because at some point in time some one decided they did not want them AKC registered and often that is because they broke AKC's rules which really are not there to ensure that the dogs are healthy but are there to ensure the integrity of AKC's parentage database. So any who has dogs that are not recent imports, that are not AKC registered really need to consider that though their dogs may be 100% basenji, some where back there someone didn't want to play by AKC's rules for whatever reason and one of those reasons might be that they didn't know the real parentage of a breeding.
Also, everyone really needs to remember that AKC is just a registering body. That is all, they do not in any way take into consideration health of the dogs being bred. All someone has to do is make sure both parents are AKC registered and that if they male is frequently used he is DNA tested, in order to register dogs with AKC.
Quality is determined by the standards of the breeder. It is up to the buyer to do their homework and learn what health tests are common in the breed they are considering, to learn about what socialization is required for a well adjusted puppy, and learn about what AKC, OFA, and other acronyms really mean. The quality of breeders is really a spectrum rather than a series of points. That is why it is difficult to come up with a clear cut definition of Responsible, BYB, Puppymill, etc.
Most define the basics of resposible to be
1. Will take back the puppy at any age for any reason
2. Sells pets on limited registration, requires spay/neuter of non breeding animals
3. Co-owns and mentors with any person who buys a show dog
4. Does the minimum health testing for the breed (this where some gray area comes in because different people are going to define this differently)
5. Socializes the puppies and is well versed in puppy development
There are probably more things but these are the ones that immediately come to mind.