Re: intuition vs. speed
what you're talking about is what sports scientists and coaches sometimes call "speed of anticipatation".
What this means is that the performer (in this case Tori) picks up small visual cues from the opponents posture, eye direction, hand position and so on and his or her response is based on these rather than the actual movement.This enables an apparent reduction in reaction times and therefore a more effective rsponse.
A good example of this is the return of a tennis serve.
In the recent mens final at Wimbledon Roger Federer could be seen running around the serve in order to make the shot on his forehand rather than his backhand. The ball is travelling at around 150 kilometers per hour at this point and so travels between players in a shorter time that it is physiologically possible to react. What Federer (and all world class performers do) is pick up on the visual cues mentioned above so that he can move before the ball is struck.
In my own opinion this is actually how O Sensei managed to "dodge bullets" as described in the Art of Peace (I think) and continue to perform well into old age - something that is often ascribed to Ki.