I'm not a fan of parelli at all, but I do agree that you must do whatever needs to be done in order to protect your space. I know a horse very similar to this one, I had to use quite a bit of pressure with the horse, but I'm pretty sure I didn't look quite as much like a flying monkey as Linda does. I started simple, not wanting anything to do with the horse, but demanding that my space was mainted. I got in the horses face quite a few times once they came in my space, but once the mare was out, all was quiet.
The people at the barn that I was at were horrified by what I had to do (yes, the same people scared to death of the horse). I simply told them that if everyone was consistent with this horse, it would never get to that point where I had to use that pressure. I never chased, never attacked, never even pushed, simply defended.
Some saw a confused horse, some saw a pushy horse, I saw an insecure horse that was terrified in his own skin because he had no solid herd stucture or consistent leadership through a person. Did he lack respect for people? Yes, but I'm guessing that no one ever gave him a reason to respect them.
I can't stand the Parelli program, but I wouldn't hold this video against them, I've seen more abusive videos just through their crappy riding! She definately lacked timing, grace, and calmness, but I've been around enough horses like that to understand that if you aren't standing up for yourself, you will get hurt. As far as the owner in the background, it was probably their fault that the horse got like that in the first place.
This video was meant to inflame, I know through experience that to work with extreme aggressive/invasive horses, it can't always be butterflies and roses. I would expect better timing out of a professional, but the track she was on wouldn't put me in an uproar.