It's important to highlight that the more significant variable here is probably the quality/prestige of universities within the U.S., which in turn then attracts the best talent and students around the world, rather than the other way around.
I think you may be misunderstanding my point. My comment is meant to highlight the fact that the quality / prestige of universities in the US consequently attract the smartest / most talented students by virtue of being the most highly ranked in the world.