You can still get turned down if there are too many of you in the applicant pool though, brilliant or otherwise. What I mean by that is that at least Harvard, whose website for international applicants I've had a look at, makes admissions decisions with the overall composition and diversity (in terms of background) of the class being recruited for in mind.
So even if somebody did play national-level sport in addition to having high grades, SAT scores and other extracurriculars, if the applicant pool that year had an unusually high number of such people, most of those people, despite technically being among the best, would be rejected simply because the admissions people are trying to structure a class in a way they like as the first priority rather than reward individuals just for being brilliant.
That's one reason why I think admission to top U.S. schools is more difficult than admission to, say, Oxbridge. With Oxbridge, it's very much about the individual and, as far as I know, they don't really care about making the 'class' fit together -- they just want the most academically able people rather than (in addition to academics) having X percent of people who play national level sport or Y percent of people who've started and successfully run a charity/business.
We're agreed on the main point though -- top U.S. schools are a long shot for OP (OP: I'm not trying to be mean but I have to be honest) unless he or she is related to some foreign head of state or something like that.