I think one of the things you're talking about, is what some martial artists call the 'second man', or, that there is a second person shadowing you, close to what some native indians call your 'second', but that's another story.
Man Ming is actually located on the spine, if you had a spiritual flashlight and shined it through your belly button until the light hit your spine, that would be man ming. It is actually one of the four dan tings. The aikido one point is actually the point of original chi, which is...if you make your hand flat, including your thumb, and then hold it below your belly button, now you have to make three fingers width inside your body, that is the actual one point that all aikidoka should be using.
That's closer, Man-ming.
Not being one for super amounts of data and references (others opinions) I would say that man-ming is closer to what I talk about here. Probably though, as pointed out earlier, a bit below that called yao in chinese. (physically speaking)
I posted this on the spiritual thread and that's usually why the misunderstandings and arguments occur because not many really practice this side of the art. Though they do love to argue, ha, ha.
In tai chi, qi gong, and those kind of things these concepts are quite well known in various forms. In shinto itself it is also well known and taoism. In fact the yao is said to be the power point that opens
up the man-ming and can be described as a gateway in taoist terminology, a gateway to the transcendance of the physical body.
In these things it's also related to the void, something else I point out regularly.
Now, here in this thread I go a step further and point out that the Japanese had these concepts. The concept of one point I'm sure was used by the most famous original Karate Masters and Koshi is so well known it's embedded in the culture. I guarantee Early Sumo knew about it and also that Ueshiba and his nephew used it but just referred to it as lowering the hips or sinking the hips but the words they would use would obviously be koshi. I also bet they emphasized it but those into only physical would not see the significance.
I read recently how the top Karate person, master, at the time explained how he was 'defeated' by Inoue (Ueshiba's nephew) with such a soft karate strike that it led to him relearning all that he already knew. He was amazed how he dropped his hips and this gave this unexplainable softness in his strike. Thus he went on to learn from Ueshiba and Inoue and put that into his Karate.
The nearest I see most Aikido folk who don't know get to it recently is some I/P they are learning and thus the ground force would be in the general ball park.
Toheis weight underside is much to do with this and so those really good at weight underside would be in the same ball park also for it is directly related to koshi.
When I see movies or joke with students about doing the horse stance, get them doing it, like they are sitting on an imaginary stall and straining their thigh muscles trying to hold the position, then I say how this is actually an exercise of 'sitting in koshi' and koshi is like sitting on a super soft cloud or sofa. Only then will the thighs relax and the true feeling be experienced.
Sitting in seiza one should be sitting in koshi too.
Like your second person analogy and indian story. No doubt they have their ways of putting it, probably the shamen of various African Arts have their versions too etc. I would expect all arts from various cultures and peoples tracing back you will find these various 'centers' of .spirit/mind/body put in their own ways.