I had heard all the 'legend' and mystical discussions about no touch throws. At Shodan (Ki Society) I started training with a senior student of Imaizumi, and the man himself. One of the things that impressed me was that no touch throws were not just talked about as mystical stuff but practiced as a more finesse version of some techniques. Plainly done and practiced. A more sophisticated version of your usual stuff.
The thing that was very interesting, was that the techniques as practiced did not change when done no touch style. The timimg and tempo did, but the techniques themselves really did not.
Another difference from what I had been training in, is that Imiazumi does emphasize moving techniques from the start of your training. The transition from moving style or 'come to hold' made the transistion to no touch natural and logical. It was not done on every technique, but where you could execute a no touch, it was based on being held, or someone coming to hold you. The other part of this approach was that if you moved to slow (or late) in a no touch, all that happenned was that uke made contact, and you executed the technique the same way.
From a strictly physical standpoint, the no touch throw puts you in a place to smash someone in the face or head - so they usually move their head or stop it from moving, the feet continue forward and you get a throw. I jokingly tell my classs, that the 'missing' O'Sensei video's are when he was smashing all the ukes, whom now move their heads to avoid being hit, and falling from the loss of balance. Truthfully most had trained in other arts, and understood the implictions of a fist being waived at your head.
For the student who doesn't or can't react - we would typically lay your palm on his head and move it out of the way for him/her, knocking them down without hitting them.
From an internal training standpoint, if you get a committed attack, you should feel like the uke has 'radar lock' on you and you lead him from that connection.
If it is of real interest to you, I suggest you find someone who can teach it in the sturucture that Imaizumi, and his students do. But it will change your Aikido.
I see where you coming from here and I believe that some are getting confused over the term throw. You are stating here if I am reading right, that if a person is moving to avoid a strike and looses balance in this action and lands on the floor, this is classed as a throw. Where as others are stating that to throw someone with a throwing technique you can only do this through making contact?
Personally if someone was attempting to strike me I'm not going to lean back in such a way as to loose balance to avoid it, I'm going to intercept that attack/block it and strike/throw them.
I wouldn't class what you are saying as a throw, as you state you are attempting to strike someone in the face.