This is the seemingly paradoxical finding of Joseph Soares' The Privilege of Power. This study is primarily about Yale, but applies to other universities and colleges at the top of the status hierarchy. A kid with perfect SAT scores is more likely to get turned down at Yale than at a state university or a second tier private college.
There are several reasons for this. First, the SAT is not actually a very good predictor of how well kids will do in the top colleges anymore. The test was never a great predictor -- never as good as high school grades, for example. These days, the Yale pool is so chock full of super test takers, and Yale College is so saturated with grade inflation, that there is not enough variation between the two scores to predict anything. So it makes sense that the top schools use the SAT less.
Second, what the SAT is better at is indicating family wealth. Two thirds of Yale's students still come from rich families, even after the supposed meritocratic revolution. Yale could fill the entire college with rich kids with high SAT scores. Since it wants some diversity in its student body, and since it wants to get all kinds of leaders, not just the rich ones, it makes sense that Yale bumps some high scorers to get lower scorers who bring something else to the table. This includes athletes (who get the most preference) and legacies (alumni relatives).
Third, the top schools have so many more fantastic applicants than they have spaces that they could apply all sorts of selection criteria besides academic achievement, and still end up with an academically stellar class. The admissions dean at my alma mater, Swarthmore, has said that he could pick five first-year classes out of each applicant pool, with no overlap, and each one would make a great class. Yale, in response to this overwhelming demand, has recently announced that it will create a new undergraduate college.
The seeming paradox is that the most "academically selective" schools are actually less likely to select solely on academics than the somewhat less academically selective tier below them. Most of this "paradox" is really just the crudity of the standards and terminology of college rankings. What the top colleges say they are trying to pick are not the best students -- all their students are above a high threshold. What the elite schools say they are trying to pick are future leaders. And future leaders are not all high test scorers.