I think I see what you mean, but these two statements are contradictory. At least in practice, an uke who refuses to move may be stable, but usually is not in a position from which they can fight back.
The classic "immovable uke" -- someone who clamps down on your wrist and grounds out -- does not strike me as particularly helpful, either for training against "real" attacks or for actually learning anything about aikido. Even (perhaps especially) in static practice, uke needs to be sensitive to what nage is doing and respond in a way appropriate to nage's skill level.
Uke should want to keep his center; there's no stiffness or tension or clamping down in a muscular sense implied. Just like in push testing you don't keep your center by going stiff, same same with uke.
If tori wants uke to move then tori has to put uke in a position where moving is his best option or where he has been put in motion by tori. Uke is training his centre just as much as tori and shouldn't do anything to give it up. I don't when I'm practicing/teaching, if he's not taking my centre he's doing something wrong and rather than adapting to the wrong thing I'd rather stop and see what the mistake is and put it right.