You would be exempted from living on campus.
https://housing.osu.edu/living-on-campus/fees-contracts-policies/housing-regulations-terms-conditions/
Although I see the point that OSU is much higher ranking than the best of the HBCU’s. You can get into great grad schools from all the HBCUs. Some examples from my family: Fisk to Cornell, Howard to Harvard, Spelman to Penn, Tennessee State to Vanderbilt and Hopkins and I could go on and on. . .
CC’ers generally advise students to go to lower ranking schools over taking out loans, funny how that changes when HBCUs are involved.