It is part of why I cannot stand to watch English riding. I assume the horses get used to it, but I've ridden my own horses for years without ever making them look like that! And in this case, she is obviously balancing using the reins to support her.
If you are in balance WITH your horse, you don't need the reins for support. And yes, you can stand in the stirrups and canter around BALANCED without using the reins to help you. If you can't, you shouldn't be in the Olympics!