Lord help me, I agree with Mike. If you trained and trained and found your body increasingly responding to martial cues without your conscious direction, in the same way your steps catch you from falling without thinking when you stub your toe walking, a traditional mind might very well ascribe the action to some outside "divine " direction. The reason for ascribing them to "divine" causes is in what was not perceived. "Spooky" things (or divine, take your pick) seem to violate causation -- almost the definition of nonlinear systems. It is very much about ascribing causes to action that we can know in result but not directly in operation.
Just to be clear, I'm not quite talking along that line. In the wider Asian view, things like a pendulum swinging in your fingers when you ask it a question, automatic writing, "intuition", a woman lifting a car off of a child in a wreck, etc., are a valid part of ki/qi and also can be construed as "possession". In the same vein, the ferocious strength needed in an emergency, in great anger, etc., can be ki or it can be a form of possession. It's hard to delineate, sometimes.
Some groups, cults, etc., tend to try to develop these "powers" and the question is "which is ki/qi and which is 'possession'?". There is an attendant discussion about ghosts, 'evil spirits', ancient warriors, good spirits, and so on. All of this is part of a known set of phenomena in Asian cultures, both in the past and in recent history.
We in the West have various overlapping ideas in sympathetic magic, pendulums/oracles/automatic-behavior and so on. There is a peripheral discussion of some of these things in Julian Jaynes' book The Origin of Consciousness in the Breakdown of the Bicameral Mind
Now what was this bicameral mind? Jaynes briefly discusses brain biology--in that there are three speech areas, for most located in the left hemisphere. They are: (1) the supplemental motor cortex; (2) Broca's area; and (3) Wernicke's area. Jaynes focuses on Wernicke's area, which is chiefly the posterior part of the left temporal lobe. It is Wernicke's area that is crucial for human speech.
Pursuing the bicameral mind, Jaynes focuses on the corpus callosum, the major inter-connector between the brain's hemispheres. In human brains the corpus callosum can be likened to a small bridge, a band of transverse fibers, only slightly more than one-eighth of an inch in diameter. This bridge "collects from most of the temporal lobe cortex but particularly the middle gyrus of the temporal lobe in Wernicke's area." And it was this bridge that served as the means by which the "gods" who dwelled in one hemisphere of the human brain were able to give "directions" to the other hemisphere. It is like thinking of the "two hemispheres of the brain almost as two individuals." Hence the bicameral mind! [Ibid, p. 117]
Archaic humans were ordered and moved by the gods through both auditory hallucinations and visual hallucinations. The gods mainly "talked" to them--but sometimes "appeared," such as Athene appeared to Achilles. And "when visual hallucinations occur with voices, they are merely shining light or cloudy fog, as Thetis came to Achilles or Yahwey to Moses." [Ibid, p. 93]
Jaynes believes in the mentality of the early Mycenean that volition, planning and initiative were literally organized with no consciousness whatsoever. Rather such volition was "told" to the individual--"sometimes with the visual aura of a familiar friend or authority figure or 'god,' or sometimes as a voice alone." [Ibid, p. 75]
Now Jaynes thinks the great agricultural civilizations that spread over much of the Near East by 5000 b.c.e. reflected the bicameral mind. These civilizations were rigid theocracies! They were reminiscent of the Queen Bee and the bee-hive. These bicameral societies reflected "hierarchies of officials, soldiers, or works, inventory of goods, statements of goods owed to the ruler, and particular to gods." [Ibid, p. 80]
Jaynes contests that such theocracies were the only means for a bicameral civilization to survive. Circumventing chaos, these rigid hierarchies allowed for "lesser men hallucinating the voices of authorities over them, and those authorities hallucinating yet higher ones, and so" to kings and gods. [Ibid, p. 79]
But in relation to ki/kokyu skills, I can see a probable connection and pathway to the way the skills would have been perceived by some people as quasi-religious "possession", kami, and so on. It's an interesting thought. On the other hand, Tohei's description of unliftable body, in that AJ interview, was simply sinking the center... very pragmatic. So not everyone in Japan looked at these skills as metaphysical.
It's an interesting topic.