I was delighted to see Monty address this problem.
For years I have struggled to teach young riders the difference between controlling the horse's head vs. controlling his legs. I.e: "You can't make him walk into the corner by twisting his head in that direction - you will just help him pushing away from it."
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The lesson got even more interesting as I watched Monty canter Chrome down the side towards the corner.
I'm familiar with Western riding - if not down to the "finer points" - so I know there are differences between it and English dressage style. Like for instance how you tackle a corner. (Seeing how Western riders ride it on a long rein while an English rider "supports" his horse more.)
So, if I may, I'd like to comment just a bit on the lesson from the English point of view.
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I could tell from the very first steps that Chrome would cut the corner because he was cantering on two tracks. His hind legs were well inside of the track and his head a bit to the outside.
In my world, that horse *has* to cut that corner in order to get around without losing his balance. Or else, he needs to get a lot more weight on his haunches and make a "show jumper-turn". Even then, he still needs to be more straight to cut it - which Chrome was in the last attempt! Cantering on a single track and a much nicer turn in balance. Love how clearly the difference was shown.
I'm guessing that Monty's schooling session - among other things - helped Chrome get that lazy right hind leg beneath him.
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I am also very happy how clearly Monty showed what happened when you pull the horse's head towards the outside! This is what I have been going on about for years.
Now, I can't make novice riders canter in tight circles in the corners - plus they are too inexperienced to school a horse in the proper way - but the basic idea of shaping the horse's inside and push him out, rather than pull, is the same.
I'd love to be able to show this vid to them.