This is "not even wrong."
Residential life is part of the package of top-tier universities - you live in the dorms first year by default, and are usually required to. When students migrate to nearby apartments depends, and is sometimes never.
Financial aid offices "meet demonstrated need" and don't typically differentiate between tuition, fees, and room and board.
If a student with a full ride moves off, financial aid cuts them a check for living expenses. Sometimes this amount is calculated based on the expectation that the student will work a campus job (with govt-subsidized wages - Work Study) and sometimes not.