My oldest graduated in 2002. He had a close friend that had great stats. This friend had 1600 in one sitting, a 35 ACT, 5 SAT IIs all with 800 accept for writing which was 750 or so. 3.97 uw GPA (he got a B one semester in 11th grade English. He took every AP the school offered. (This is an urban public without a lot of APs.) In addition, he took 4 classed at UW-Madison - multivariable calc, differential equations, and 2 computer programming classes - where he earned all As. He participated on the math team for 4 years, was on the soccer and rugby teams, and played bass in the school orchestra. He was also very active in his church and had lots of volunteer work through that.
He was turned down outright by MIT. Who knows why? He is a great kid from a state that doesn't send a ton of kids to MIT. He interviews well, has multiple interests, had a ton of awards... I don't know if MIT was his first choice honestly and maybe that showed through on his application. He graduated from Carleton in 2006 and is now in a PhD program for math. He is quite happy and had a great college experience.
So, I don't know the answer to your question. We know that at the upper levels, college admissions can be capricious. Had my son's friend did not apply to any of the Ivy schools. If he had, I am willing to bet he would have had some acceptances, but we will never know. I think Carleton was his top choice all along. Ultimately, kids with top scores will be accepted to some wonderful schools as long as they are willing to look outside of the Ivies.