MIT, Stanford, Harvard, Princeton, and I believe most or all of the other Ivies, all fund 100% of the demonstrated financial need of every student, and they do not consider the financial needs of applicants when making admission decisions.

No, not for international students. Stanford (I haven't checked others) is very explicit about having a limited number of scholarship for international students: https://financialaid.stanford.edu/undergrad/how/internationa.... Admissions for US applicants are indeed need-blind.

> demonstrated financial need

Higher education is a strange purchase that is engineered to extract the maximum amount of money (up to full-cost tuition, fees, etc.), based on financial records which you are forced to provide.

Any asset except for a residence is typically considered something that could be tendered to the university, and is accordingly deducted from financial need.

This means that external scholarships are limited as to how much they can reduce the expected parental or student contribution. Anything beyond this limit is deducted from need and pocketed by the university.