Wow, that's actually a great video! I've been looking for something like this.
And I cannot say how much it irks me to hear people talking about needing a harsher bit. No, no, NO! If you need a harsher bit, it means there is an error in the rider's training or the horse's training and you need to go back and fix that. A harsher bit may seem like a quick fix, but it's only temporary and puts the horse through more pain... especially if the rider does not know how to use such a strong bit properly.
The fact is, a bit does not control a horse. The bit is a tool for communicating to your horse, but really, any horse is perfectly capable of running through the bit if they want to. The point is that a stronger bit is not the solution. After all, we want a horse seeking contact instead of avoiding it, right? A harsh bit does not encourage the horse to seek contact; it simply forces contact upon him (of course meaning if it isn't used correctly. Then again, if the rider could use a bit correctly, why would she need a stronger one?)
Anyways, I'm done my little rant.
And yes, it will take some time for the horse to learn to engage his hindquarters and back. It takes time and training (on both the horse and rider's part). A harsher bit is an easy substitution for hard work that in the long run really doesn't fix anything.