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At Harvard and MIT "need-blind" means that all admitted students receive a financial aid package, adjusted for the student's financial means, to make it work somehow. It's a combination of grants, loans, and presumed income from on-campus part-time jobs. At some other places "need-blind" may simply mean that admissions are granted regardless of financial needs, but financial aid is not guaranteed. Yes, federal grant and loan programs are not available to international students, but the universities have other resources (endowments, private loans, etc.)

As for sources... I am a former international student at a top US university and I know many others too. Almost no one I've met came from a rich foreign family.