This is not an accurate statement. Only a small number of schools are need-BLIND for international students, meaning that they don’t look at whether or not an international student can pay anything when deciding whether to admit the student AND then promise to meet the full need of the student (even if it’s $80k/year). There are many schools that are need-blind for international students (all public schools, for one), but they won’t promise to meet your financial need. And then the schools that do promise to meet an international student’s need, they aren’t as wealthy as those 7-8 schools, so they are need-AWARE when they select a class, because they don’t have enough money if they accept a lot of students who can’t pay anything or only can pay a small amount.
It’s great that you’re showing flexibility. The more flexible you can be, the more options may end up opening up for you.