And yet- knowing that the origin of TBs was the three foundation sires bred to local mares, and knowing that all color variations of horses have long existed in Europe and around the world, I think it's silly that the Jockey Club says 'nope, can't happen.' Because it can.
In fact, kind of in the same vein, in the early years of the TB as a breed, many race horses were gaited due to those initial crosses. They'd gait to the starting line, gallop the race, then gait on back to wherever they needed to go. I have never known a tb that 'could' gait but knowing that it's back there in the gene pool, even centuries back, you can't rule out real longshots!