It occurs to me, and shamefully only just as I type now, that learning/teaching the piano should involve an awful lot more 'showing' than it often does, both listening and seeing.
What you are probably describing is the effect of "mirror neurons", special neurons that show activity both when a subject performs an action and when it observes the same action performed by itself or another. In effect, you get brain and ever so slight muscle activity exactly mimicking what a virtuoso would be doing on stage, somply by observing. I think as time goes on more research will be done on this and it will become a larger part of perfromance/learning.