As others have stated, I think you're missing the medical DoDMERB requirement separation from DoD functions versus University requirements. Being an undergraduate student in the Corps of Cadets at either university is more similar than different in terms of requirements and future paths. DoDMERB qualified is required for contracting with a service branch to commission - by default any ROTC scholarship requires you to contract thus you have to be cleared by DoDMERB. The military aspect of The Citadel and VMI is the regimented schedule and customs of living within a military environment and you are required to take 4 years, all 8 semesters of ROTC - if you aren't on scholarship with a specific branch, or aren't pursing a contract (trying earn a commission) you can pick one to satisfy the school's requirements. You mentioned AFROTC and I know that the AFROTC programs will allow non-contract, non-pursuers for the first two years (GMC) of ROTC courses BUT going into your Junior year you have to have an enrollment allocation to commission when you graduate (two years away), have to attend Field Training between Sophomore and Junior years and will sign your contract with the Air Force to move into POC which are the last two years of AFROTC. So, by the end of your Sophomore year you'll have to have DoDMERB clearance to continue with AFROTC. If you don't, at The Citadel and VMI you'll be switching to a different ROTC branch, likely Army, for the last two years of school.
As far as medical requirements, without knowing what your DQ cause is (please don't share here, not needed)... The Citadel does have academic and physical acceptance requirements, I'd assume VMI does also. They are very likely much more lenient than DoDMERB since the expectation is that you are able to do the PT and perform cadet duties not that you have to qualify for military service, future deployments, etc as would be expected of military officers coming out of ROTC on a commissioning path.
Summary - these are two military colleges not service academies and you can complete studies, earn a degree and take ROTC classes without DoDMERB qualified status achieved.