I just found an interview of Tohei by Aikido Journal, in which Tohei specifically states that he got the key (pun intended) from his sempai Tempu Nakamura (who was, in Tohei's words, "a yoga master and psychologist").
Here's the bit I found:
When I went to Hawaii and tried to use the techniques I had learned from Ueshiba Sensei, I found that many of them were ineffective. What Sensei said and what he did were two different things. For example, despite the fact that he himself was very relaxed, he told his students to do sharp, powerful techniques. When I got to Hawaii, however, there were guys as strong as Akebono and Konishiki [two well-known Hawaiian sumo wrestlers] all over the place. There's just no way to use force or power to prevail against that kind of strength.
When you're firmly pinned or controlled, the parts of your body that are pinned directly simply can't move. All you can do is start a movement from those parts that you can move, and the only way to do that successfully is to relax. Even if your opponent has you with all his strength, you can still send him flying if you're relaxed when you do your throw. This was something I experienced first-hand during that trip to Hawaii, and when I returned to Japan and had another look at Ueshiba Sensei, I realized that he did indeed apply his techniques from a very relaxed state.
While I was with Ueshiba Sensei I was also studying under Tempu Nakamura. It was he who first taught me that "the mind moves the body." Those words struck me like a bolt of electricity and opened my eyes to the whole realm of aikido. From that point on I began to rework all of my aikido techniques. I threw away techniques that went against logic and selected and re-organized those I felt were usable.
Now my aikido consists of about thirty percent Ueshiba Sensei's techniques and seventy percent my own.