One reason for the big whites' high resolution property is that lens resolution is a function of diameter; a larger diameter lens (for a given focal length larger aperture lenses have larger diameters) will resolve more than a smaller diameter lens assuming similar correction for lens aberrations. See http://en.wikipedia.org/wiki/Optical_resolution and scroll down to lens resolution. There are other aspects of resolution as well that are discussed in the article. Lens aperture is just one part.
I don't believe it and I don't care. I would definitely consider a 400mm/5.6 lens with 4-stop IS and IQ at least as good as the current 400mm/5.6 ... if price was less than USD/€ 2000 and would not waste a single thought, whether or not a 400/2.8 II IS would offer still marginally better IQ @ f/5.6 ... or not.
You are right not to believe this and not to care. The original post is a bit misleading. From the wiki page:
"The ability of a lens to resolve detail is usually determined by the quality of the lens but is ultimately
limited by diffraction. "
"Only the very highest quality lenses have diffraction limited resolution, however, and normally the quality of the lens limits its ability to resolve detail." This is the case for the lenses that mere mortals can afford. Since accurate design and production of a large aperture lens is much more difficult, the main difference you will see is light gathering ability and shallow DOF, not necessarily resolution. This reveals itself in the fact that most lenses get sharper as they are stopped down a bit : it is the aperture size used to take the image that limits the resolution that the lens can provide, not the maximum available aperture of the lens. A perfectly designed and built lens should perform worse as the aperture is reduced, but in real life, this does not happen. Reviewers of the 400 2.8L IS II say that the IQ does not improve as it is stopped down, but it doesn't get worse either. Maybe the sensor can't pick up the differences.
My bet is that Canon could design and build a 400 5.6L IS that could produce images every bit as good as the 400 2.8L IS (stopped to 5.6), of course much lighter and cheaper. Light and cheap means you're more likely to have it with you.