Re: Spill over
In my perception, what one is learning is how to do things that the teacher is enacting within his own body and transmitting into his uke's body on contact. Uke's body is compelled to move in a mirror set of motions that are amplified versions of what has been created in nage's body, like cogs and gears on a locomotive. If uke is intuitively astute enough, over time and repeated exposure, he will be able to duplicate them.
So, teaching/learning can be by feel, with a minimum of verbal or systematic instruction. In some internal training traditions, some people learned their skills almost wordlessly, by sensation and feel, perhaps in some cases combined with a very cursory and simple set of physical instructions. I wouldn't call it osmosis, but a body intelligence that can sense and parse out complex sensations and positionings, and duplicate them.
However, I do believe that this is why, to learn aiki, one has to have repetitive experience with an adept and willing teacher, at a slow enough rate at first for the student to perceive and parse the sensations. In that respect, it "has to be taught." A person who does not want someone to learn aiki, will not provide the opportunity. They will demonstrate on you, using rapid applications you don't have time to fully sense out and parse where they're coming from, and how.