There's
another thread regarding knives going on in the Self Defense forum.
Right now, today, I see kata as a demonstration of principles. So, what does the knife defense work in san kata (
techniques 17-24) show us? To me, san kata is showing us concepts to defend against the weapon. If the knife is coming from concealment or swings back to gain momentum, close and take control of the knife. Otherwise, stay away from the knife and create space. I've seen other systems that have a much different take on empty hand vs. knife -- some of it is complete crap and some of it is pretty nice.
The situation you describe in closing sounds very much like Adam's encounter. The situation ended up with the bad guy stabbing himself a couple of times and then pulling violently to get his weapon hand away. This is how kote-gaeshi works in the real world, and the people with no ukemi skills often land poorly. This poor chap landed on his head.