The Ivies report that they hold the same standards as they do with US citizens. However, because there is a limit on the number of foreign students admitted, the admission rate for foreign students is significantly lower than the admission rate of US citizens. All they state is you must score the highest grades and ACT/SAT, take challenging course work, and be academically at the top to at least pass the threshold. I know Yale (and I am sure Harvard, Princeton, Stanford-I know Stanford is not an Ivy. But a few years ago, it's admission rate was lower than Harvard. Now, they are both at 5%) have commonly rejected students who have perfect SAT/ACT and are at the top of their class. I also know, even if you are wicked smart, you must have something else other than just grades and scores; something to set you apart from all the wicked smart kids.
My daughter's grades and scores above would likely not be admitted if it were not for the letter of support she received from the coach.
I'm posting here from my perspective as an alumna of an Ivy League school who was accepted as an international student on academic merit (my daughter is the athlete, not me! ) What they don't tell you on the websites and school literature is that for international students, it is NOT a needs-blind admissions process. You MUST submit documentation WITH your application that you can pay for not just tuition, but also room and board/cost of living expenditures at the school. You will not be allowed to work in the US during your course of study; although international students can be granted work permits to work at the university (in labs, libraries, dining halls) these jobs pay nowhere near enough to support you through college. This doesn't mean that you or your family need to have the money in a lump sum in the bank account (although this is certainly acceptable evidence to the Ivies of your ability to pay, and for many international students that I knew, was the preferred way of demonstrating ability to pay); many of the international students I know demonstrated their ability to pay via documentation of grants and scholarships secured from their home countries' governments. This would entail knowing how to work the bureaucracy of both your own home government's educational system as well as the US's (and, of course, having a home government with money of its own to spend on its young citizens!) So for foreign applicants to the Ivies, I don't know how much you can count on getting any of the sports scholarships unless you were Olympic level for your home country, and if you were an Olympic level gymnast, you're probably going to a D1 school, not an Ivy.