That video is complete and utter crap. Just one more person that has the fanatical viewpoint of "OMG, if you ride with a bit, then you must be yanking your poor horse's head off, you big meanie-doo-doo head!!!."
In every single clip in that vid, the problem is not the bit at all, it's the person holding the reins. They would be hurting the horse just as bad in a bitless bridle or a halter as they are with the bit because they are sh**ty riders; nothing more, nothing less.
Why it is so hard for people to grasp the concept that some miracle contraption that you put on the horse's head will NOT correct bad hands or poor riding. Bad hands and poor riding are uncomfortable/painful for the horse regardless of whether he is being ridden in a spade bit or a nylon halter.
There are lots of people out there that are much harsher with their halters or "bitless bridles" than I would ever dream of being with a bit.
So I ask the question, which option is better, regardless of headgear on the horse: A person yanking on the horse because of crappy hands and the unwillingness to learn to be soft or a person who works their ass off to learn how to be soft and giving with a well timed release?