I'd note that nobody has argued against the validity or utility of moving around, evading, jumping, dodging or any related action as a martial tactic. If you watch Shirata (the source of that "immovable body" quote) you'll notice that he moves about quite a bit.
The difference of opinion comes as to what the definition of "Aiki" is - saying that "Aiki" isn't evasion doesn't mean that evasion is wrong, or even inadvisable. Donuts aren't "Aiki" either, but where would my day be without them?
To the people who think that all definitions of "Aiki" out to be accepted, that it's all good, what if I said something like "I was walking down the street and I turned to a teenager who was annoying me, kicked him in the nuts and broke both his arms, what wonderful Aiki!". Wouldn't you feel obligated to say something?
"When an opponent comes to attack you, you just move your body slightly to avoid his attack, and let him go wherever he wants. This is Aiki. In other words, you give him freedom." - Morihei Ueshiba
So is he wrong then?