Even though it is absolutely necessary and sometimes even lifesaving for horse people to be able to handle escalating situations, I don’t think it lies at the heart of horsemanship. What lies at the heart of horsemanship is the ability to work every day with horses in a way that abilities to handle emergencies are very rarely needed.
In equestrian sport there is one thing specifically that tells a lot about the quality of riding, namely the horse’s mouth. A contact that is pleasant and practical for both parties is a skill and accomplishment that is the essence of riding.
Sometimes a horse behaves in ways that humans find incomprehensible or surprising. The thing which guides a horse in its behaviour, regardless of the situation, is always what, from the horse’s point of view, is the most rewarding or beneficial to it. In efficient training the trainer uses the things the horse considers rewarding as reinforcement.