The Appy, as bred by the Nez Perce, would demonstrate an ambling gait (sometimes called the "Indian shuffle") with some regularity. The Tribe seemed to value this gait and these types of horses were not uncommon. There are documented instances of the horses being sold to outsiders (the Nez Perce being one of the very few tribes that engaged in professional breeding of horses).
After the defeat of Chief Joseph the Army ordered the Appy stallions destroyed and replaced them with draft-type stallions (as part of the program to turn the warriors into farmers). At least 1200 were destroyed (and I've seen numbers claiming more than 2000 were killed). A couple hundred survived, either because they were secreted or were just being pastured in out of the way places and the Army never found them.
In the early part of the 20th Century a group of Appy enthusiasts determined to "rejuvenate" the breed. According to what I've read (and some oral accounts by Appy historians) there were able to acquire a reasonable number of pure blood horses. Still, the numbers were small and that raised questions of lack of genetic diversity. So a number of known mixed-bloods were accepted into the newly established Appy registry, based upon inspection and the horses being of the correct type and coloration.
One thing they did not accept was the "Indian Shuffle." At that time many knowledgeable horse experts opined that any "ambling gait" was the result of lameness. Our local 4H Horse Project coordinator lent me an old text on lameness years ago and this statement was clearly in the mainstream of thought in the early 20th Century. She knew we had Walkers and the time and that I'd find it "amusing."
In reality, there are some lamenesses of the trotting horse that manifest themselves as a "pseudo-amble." The base premise (that the amble is a defective trot) is false. That doesn't mean it's not believed even today in some places.
My Appy friends tell me that their Association is not friendly to the "Indian Shuffle" even today. If the gait manifests itself (and it sometimes does) it's not talked about and the horse is quietly "moved on down the road" sans papers.
A number of Walker folks have crossed Walkers and Appys, producing the "Walkaloosa." There's also a "Tiger Horse." Read about it here The Tiger Horse Registry
As with all "breed propaganda" be careful with claims that sound a bit "stretched."
We've boarded some Appys over the years. They were not "special" in any way I could tell beyond their coloration. QH types seem to have a lot of "heartburn" with Appys and love telling Appy jokes. Such as:
Q: Why did the Indians ride Appys? A: It was the only thing they could catch by running after it.
Q: Why were the Indians so cruel in battle? A: 'Cause they got there riding Appys.
Of course the Appy folks have some, too.
Q: Why don't Cowboys use Appys? A: 'Cause you have to be smarter than the horse to ride one.
There are LOTS more.