I think some - like Howard - get a fair amount of decent (maybe not excellent) students who want to avoid debt. Sure, Harvard, et al will give a poor kid a full ride, but the child of a still married cop and nurse is too rich for meaningful financial aid at even the most generous of the financial aid granting institutions. And if the parents are smart, they'll make sure their bright kid chases merit money so as to keep the loans to a minimum.
Howard and Hampton University (in Virginia) are two of the more successful HBCUs. Both have solid academic reputations and they’ve been creative in developing additional revenue streams for the institution. Howard owns WHUR-FM, one of few commercial radio stations owned by a college or university, and it’s always near the top of the ratings in Washington, D.C.
Hampton operates a proton therapy institute that attracts thousands of cancer patients each year and they were the first HBCU to open a pharmacy school. The great irony is that most African-American students, as products of “government schools” can’t meet admission standards. So, white and Asian students make up about 50-60% of each incoming pharmacy class. Hampton is happy to have them as students (tuition is $30K a year) and alumni who can give back to the institution.
Admittedly, I don’t spend much time on the Hampton campus, but I’ve never heard anyone at the school—black or white—complain about the disproportionate number of white students in the pharmacy program.