Misunderstanding 1: The inability to focus at small apertures is nothing to do with amount of light. You still have a lot of light with f/8 in sunny day, much more than at f/2.8 indoors. It is actually related to Phase Detection AF mechanism which operates much like range finder comparing images from different angles to determine it’s in-focus or not. Small lens aperture just blocks light paths from different angles, and as the result, makes AF sensor unable to work reliably or not at all.
Misunderstanding 2: Older Nikon cameras may not auto-focus reliably with a lens having a maximum aperture smaller than f/5.6. That may sound bad, if you assume that it means the camera will not auto-focus reliably when the aperture is closed down to f/5.6. That is not what Nikon is saying! Instead they are telling us that auto-focus may not work reliably on older Nikon cameras with a lens having a maximum aperture of f/5.6, with the emphasis on the word maximum.