It is interesting that while nage's mindeset should be one of mushin (not concentrating on anything, yet ready to deal with anything) uke's mindset must be much more cerebral and full of intent for Aikido to work.
The attacker mind (basic techniques):
On another forum we were discussing why beginner Aikidoka have troubles performing Aikido on non-Aikido practitioners and we all agreed that the primary mistake is to try and perform a technique on them. When you do that you change uke's mindset from a single-minded attack mode to one of "I'm going to resist whatever you are doing to me" mode, and thus it doesn't work. As soon as you relax your mind and use the principles (rather than thinking about a technique), uke is able to stay focused on his/her attack and the more intent uke is one attacking you the better your Aikido works.
The attacker mind (intermediate techniques):
Instead of letting uke actually get a hold of your wrist or shoulder, etc. -- you stay just a moment ahead and lead uke's movement. Uke begins to try harder to "get" nage, overextending themselves a little more each time. Now you are able to throw uke without letting them touch you.
The attacker mind (advanced techniques):
When Watenabe and other sensei throw uke with "no-touch" it is a lot less magic and lot more real than people are lead to believe. It is an extension of leading. When uke is so absorbed in "getting" nage, nage can disturb ukes' mindset rather than his physical balance - striking his hand out in the direction of uke's face and uke will fall down. It isn't that nage has used magic, it is that uke is so committed and entranced in his/her attack-mind that any interruption is now unexpected and his/her mind and body react instinctively by repelling from the unexpected motion.
I personally have fallen pray to "no touch" falls, and I can tell you that I try hard to make my attacks connect (sensei know that if they don't block they are getting hit) -- buts it my intent to attack (my full commitment) that provides the very fuel for the "no-touch" throw. Quite a few times I have wound up on the ground wondering what just happened, with everyone else smiling (including sensei). When I ask others what he did they say, "Nothing, he didn't even touch you"
The reason it doesn't always work on newbies is simply that they don't always have a committed attack mindset -- in which case (as I have always said) the defense against a non-committed attack is do nothing (since you are in no danger) -- so it did actually work!
So you are right that the attacker's mind must be "thinking" (or full of intent) in order for it to work. I forgot to mention that timing is essential - true blending with uke' movement (and mind) in order to make it work.
Now as for doing that 2 metres away or from a different room…I have never heard of that