It's true. For a perfect, diffraction limited, lens, the larger the aperture the higher the resolution.
In fact the resolution would be around 1600/(fstop) line pairs/mm for such a lens (I mention this in an article at http://www.bobatkins.com/photography/technical/resolution.html
The catch is that the faster the lens, the more difficult it is to correct all aberrations and spherical aberration is usually the killer for very fast lenses. Stopping down reduced the aberrations, especially spherical aberration. Few, if any, photographic lenses are diffraction limited wide open. Maybe something like a 500/4 or 600/4 could be close.
There are diffraction limited lenses - typically very expensive telescopes - but they are rarely faster than f5 and usually much slower.