> There are two related, but different behaviors here, which both happen
 > when the current buffer is killed:
 >
 >    . which buffer becomes the current one, and
 >    . which buffer replaces the current buffer in its window
 >
 > The manual's documentation of the behavior of kill-buffer which you
 > quote talks about the former, whereas switch-to-prev-buffer-skip
 > affects the latter.

Indeed.  By virtue of the fact that the command loop makes the selected
window's buffer current, a user gets the impression that these are one
and the same.

 > So I don't see a problem in the documentation, and AFAIU the
 > correction you suggested for the manual is incorrect, because it
 > wrongly conflates these two subtly different behaviors.

We could say

   If you kill the current buffer, Emacs makes another buffer current and
   either shows another buffer in every window showing the old current
   buffer or deletes such a window.  If you are not satisfied with that
   behavior, try customizing the options `kill-buffer-quit-windows'
   and/or `switch-to-prev-buffer-skip'.  In either case, the command loop
   will eventually make the now selected window's buffer current.

instead.