Awfully familiar actually. I read a quote by Morihei Ueshiba in an interview once, someone (wish I could remember who) was being interviewed and said that the founder would often say things like "A man stands between the Heaven and the Earth", which the person being interviewed viewed as a rather outlandish way of saying 'stand up straight'. He was likely correct in that what the founder probably meant was 'stand up straight', but he had some other things in mind too it seems. When I teach these things I usually try telling people to stand up straight and make themselves as tall as they can, then allow yourself to relax downwards from that posture.
I usually tell people that if a limb is being moved you have to imagine the tester isn't actually trying to move your limb, but they are in fact trying to move your centre, similar to what you described. The advantage that the many different ki tests have is that they put you in a variety of body positions both static and dynamic which make such coordination difficult, usually if you try to concentrate on copying only the movements you will fail the ki test. Often once you start to get the basic idea and can do the simpler ki tests you fail the tests which involve movement. You tend to be strong at the beginning and end of the movement and weak in the middle.
Who said this stuff wasn't in aikido...?