Re: Saito Sensei & the no-hands throw
I was holding on. Can't think of a specific instance where I was thrown in a horizontal arch without touching nage but I don't see how it's not possible using simple mechanics. I expect with enough practice someone could throw themselves as described without a nage at all. It might look funky, but not impossible.
In capoeira I've seen people fly in what look like impossible directions -- sometimes with a partner, sometimes solo -- and there is certainly no discussion of ki or any extra natural forces (well, it is a very spiritual art, but no talk of extra natural phisical forces). Also, look at video of Michael Jordan in the air. At times it looks like he's changing direction mid flight. I don't think ki is involved, but you'd have to ask him.
I've taken a closer look at your description and here's the thing. If uke wasn't holding on and moved as you say and it's your contention that some extra mechanical force has to be involved, it sounds like it would not be an extension of ki but a contraction of ki. Is that even possible (in the ki lore) to contract your ki to keep uke's upper body close to you while letting his legs go wide (as happens often when uke is holding on)?
When I first started aikido I had read a lot about ki and thought that that was what I was going to learn: magical (read extra natural) physical powers. And at my first dojo, there was a lot of talk about such. But even with all the incredible people I've trained with, and all the spectacular things I've see and felt, I have no direct experience of anything that can't be explained by physics and psychology.
That's my story and I'm sticking to it (until, of course, I experience something that can't be explained).