Anky was one of the proponents of 'Low, Deep and Round', training, the most extreme version of which, hyperflexion or rollkur, is now banned by the FEI. This involves keeping a horse's head down to its chest while training, which supposedly helps it become more supple, loosens up the neck and improves elasticity of paces. For years, that style of rider and trainer got very good marks from judges because it exaggerated the suppleness of a particular set of muscles, and it looked like the horse was really putting its back into the work. Doing it by force actually risks nasty injury and certainly isn't kind to the horse.
In hindsight, although hyperflexion riders made a good job of the moves required, you could often see tension in the neck, and sometimes the horse hollowed its back in resistance, which meant it wasn't moving freely. The horse often looked unhappy too, with a clenched jaw and ears back. Modern dressage has moved away from that, which is for the best, as hyperflexion was making its way down to the lower levels of the discipline too. So that change isn't entirely new, but what we are seeing from Carl Hester and his pupils, is that even more sympathetic training and riding is not only producing horse and rider combinations that can perform the moves with as much precision as the hyperflexion riders, but actually do it in a more relaxed and free-moving style.