We worried about that, too. But you just have to read the guidelines offered up by each school.
For example, Lowell states, "Families who apply for financial aid should know that both the admissions and the financial aid committees make decisions independently; however, it is a need-sensitive process." (I admit I don't know exactly what this wording means, but our kid was waitlisted there due to FA needs and then not accepted because they couldn't meet our needs.)