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.
I have no problem with anyone going to full-ride schools (HBCU or others), but also feel it might be a good idea to look locally if, like in OP’s case, she might have schools in her own state she can attend (by commuting) inexpensively.
Traveling back and forth to AK, NC, AL is not going to be free, and like @intparent pointed out OOS schools might not accept existing insurance.
As I think someone showed above, she may not have to take out loans at OSU. Also, she may not have the extra health insurance costs, and possibly lower transportation costs.
Look at the website. The advisor is wrong. Note that your insurance may or may not work for OSU. If you have a really high out of pocket maximum expense, it still might not meet their criteria. Something that would have to be checked out.
If you are polite about it, you might be able to leverage the misinformation the advisor gave you into allowing that Nov 1 date to slip (assuming that person worked for OSU).