One of those dogs is pretty strictly show bred. Is the third dog posted an APBT or not? I have yet to actually get anyone to answer this question directly. And the main reason nobody will touch this question is that, again, it forces them into a catch-22 they don't want to be in; You either have to admit that a show-bred dog is still an APBT, which then naturally opens the door to even deeper questions...or...no dog that is shown and hasn't been tested in the box is a real APBT, but then you've knocked off a whole lot of dogs from some of the most prestigious yards in history.
I suppose this is what you're asking:
I owned a puppy off of Tanya's Gr. Ch. Boogieman and Hogtown Light. I swear I thought he was a redbone coonhound pup at first (thus why he was the first dog I ever had ears cropped on...and the last). He was a great little 48 lb dog, and he turned into my main catch dog. He was an amazing hog dog!
Now, there's a large group of people that own dogs bred off of or down from Boogieman. These people have rarely allowed the dogs to get dirty, much less actually work them. They do travel and show them in ADBA quite extensively.
Now you ask, are all the dogs APBTs? Why or why not? The answer is "yes, they're all APBTs".
I bred that male to my female, a daughter of Ratliff's Ch. Butkus, and produced many fine dogs that had drive and heart and guts and brains (the brains came from the dam's side...certainly not my male. lol).
These other people are backing their dogs to other strictly show-bred dogs, with looks being the ultimate goal for the breedings.
For how long are these resulting generations of dogs, bred down two separate paths, always considered the same dog? Over time, can you grab one of those show-bred dogs and get it hunting and have it do so well, showing all the desired and necessary attributes to do so? At any time, you can take a hunting dog and put it in the show ring. It may or may not bring home that pretty blue ribbon, but for a working dog, what is the ultimate goal? A blue ribbon for it's perfectly cropped ears and square head on square body? Or a dog that can still do what it was bred to do, or at least perform in an activity that is as close as one to get to the original purpose?