While in college, I heard a very fascinating story of how Harvard retaliated when confronted with evidence. There is a linguistic professor at Penn who went to Harvard and is Jewish. While at Harvard in the 70s, he suspected discrimination and broke into the admissions office, unearthing documents proving his case. Harvard responded by sending him to Vietnam, presumably to die. Long story short, he lived to tell the tale. After the war, he went to MIT and received a doctorate. He has all kinds of interesting stories about 'Nam too, but this Harvard story is really something else.
All Ivies/Stanford discriminate, they can fill the school 10x over with Valedictorian/Chess champions if they want to. But they have to mindful of their corporate customers as well, companies want a diverse menu of people. Some studies have been done around how they discriminate now: presently the tasteful instrument of discrimination is extra-curricular activities. You'd be hard pressed to find too many Asian Americans doing Lax or Crew.
Remember, these are private institutions so strictly speaking, they could do what ever they want (Disclosure: I am Asian). The bigger issue is that many people do have to go to one of these colleges for upward mobility. These schools are like oligopolies that have taken captive the American dream.