Any dog is eligible to show in the AKC ring...white is the only disqualifying fault. Washed out colors are serious faults.
I think what people forget about the AKC ring is that you can put any dog in there...it just depends on what your chances are winning are with that dog. We all kind of know that anything but black and tan is already at a disadvantage in the show ring. I've also been told that black is tougher to win with because its easier to see faults on an all black dog. Sables aren't preferred, but I've seen some patterned sables manage championships in the AKC ring. I think a well proportioned, everything else good dog that might have a brindle pattern would easily be able to be entered in a show and win (all breed more likely).
I'm not sure if a judge, knowing the history of the breed and the probability of a brindle pattern, can ask for a DNA test if the dog is truly registered with the AKC and has a pedigree. Not sure what the process is for "challenging" the pureness of a dog is if the judge does have a question about it. It would really take a huge genetic surprise for two dogs of separate breeds and when the puppies are born the ONLY trait that a pup takes from one breed is the color while the other breed completely dominates the conformation.
CD RE TC HIC 7/10