Showing passion, interest, and recognized achievements is what we have seen make the difference for the top schools.
For example, one year every student who had applied to Columbia and subsequently made Regeneron Finalist received a likely letter from Columbia.
Likewise, it's rare for a USAMO qualifier not to get into a top school. We had a USAMO qualifier in our school this year that didn't do well (so far), but he was known as the "obnoxious kid", so that's no surprise. In previous years, the USAMO qualifiers ended up at Harvard, MIT, and CalTech.
Now there are plenty of kids who get into the top schools without those qualifications, but the qualifications make the decision pretty easy, barring something disqualifying about the application.
