Where did you hear such thing???
Selective colleges set a limited cap on no. of international students, and they dont have particular favor on international kids. Mount Holyoke, maybe, but doesn’t mean it will be easier at all.
Yes, it’s easier to get in at colleges outside the top 30 (especially LACs) if you don’t need financial aid. But you can’t “not ask for aid” in order to get in, then ask for aid later - because you’re in a different pool of applicants, you won’t be allowed to ever apply for aid. And you’ll need to demonstrate that you do have the money or you won’t have the visa. So, apply for admission only as an international who doesn’t need financial aid ONLY if you really don’t need financial aid.