Well there is a specific instance (ie, a backache) in which the koshi is used for the lower back area, but generally they're just talking about the whole pelvic region.
Not so. In martial arts and in medicine which is far more pertinent to the discussion.
Funny thing is that tai chi also has a problem with peoples misunderstanding of a similar thing they call kua or cua ( I forget which is the right spelling).
The development of Koshi I would say is one of those fundamental 'secrets' hidden in plain sight and if you prefer a 'general' meaning for it then you will never get it.