No. A university is not required to meet full need for every student who asks. There is no law that says that they have to give up their university funds to anyone.
What they do is limit the numbers of students they admit with aid packages. They may select one or two students, that particular year, to fund. You have to be the best student from your country to be even be considered for their limited aid.
This is what a need-aware school will review. If you say that you need financial aid to attend their school, they will be aware of your need. If they can’t afford you they won’t admit you with funding. They may admit you but they won’t offer you aid.
A need blind-school won’t look at whether or not you can afford to attend their school. They don’t look at your financials when making a decision. They may admit you but without funding.
The universities will explain on their websites how they calculate need.
If you have too much need they don’t have to admit you.