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?
1. First, "aiki" is used by aikido people in much the same manner as "smurf" is used by the Smurfs. I think it is a loose term impregnated with personal belief and ideology. Because of the grip on personal and ideological perspective, we are hesitant to curtail the usage of the word.
2. There are first and second-hand accounts of the usage from O'Sensei. First-hand accounts (from O'Sensei) are in Japanese and require translation. By all accounts, to the West, the usage requires a cultural filter (both social and spiritual).
I assume the consistent use of "aiki" by O'Sensei implies that the seemingly paradoxical (or at least non-linear) contexts in which he used "aiki" were, in fact, intentional. This is a big component for my acceptance of a definition that needs to be specific enough as to be a definition, but flexible enough to encompass a myriad of perspectives.
I use the term "agape", I have also heard "empathy". The ability to understand and appreciate the object and advocate its relative position. It is this relationship that empowers me to physically (and non-physically) be invested in the general well-being of the object of my empathy, while still aligning my actions with my preservation. For now, this is the concept I believe O'Sensei intended when he used the term "aiki."