By moving as Ron is describing one is moving with Uke but just slightly ahead. What the Uke wants is to strike or grab or whatever. Ultimately, one is grabbing their mind and manipulating their intention, their desire to harm you. As one progresses the circles, the leading becomes smaller and smaller. Initially, I just moved as Saotome sensei told my sensei, "Move in or out, left or right." After that by being in a safe place, say right next to them you can change as they change, adjust as they do. I let them lead, but yet stay just a little bit ahead of them. It sounds contradictory but that is how it plays out. When I do it, I feel very connected to my Uke and it also plays out that way in a randori setting as well.
I was never a believer in the theory that Aikido "takes away the opponent's desire to harm you". I much prefer to make him realize that he *can't* harm me...by taking kuzushi on-contact, and using that to control the encounter.
You mentioned Saotome. Have you seen Saotome "matching" his movement with what uke is doing? I haven't. He just enters, does his thing, and uke is thrown.
Have you heard him talk about "matching" or "blending" with an opponent's movement? I haven't.
Though I have heard him (more recently) talk about controlling uke with aiki, using yin and yang and maintaining polarity throughout the body - though that stuff probably belongs in another forum