Those sound like two different abilities, to me -- to be unthrowable vs to be able to throw anyone. Or is it that the two are closely related?
I would say that you can't really throw someone if you're unstable (well, you can, but not very well) - so by "unthrowable" I'm talking about a kind of stability training (in a sense).
If I am stable, unthrowable, and I occupy the center - the center of the movement is exactly in me, then everything else is on the outside, almost by definition. When you're throwing, being on the inside with things moving around you is generally where you want to be. Ueshiba actually said this, repeatedly.