My wife is a university administrator and they have a similar process. What they are mostly concerned about are violent or sexual crimes, not crimes such as possession or DUIs. They do have an obligation to provide a safe environment for all students so they have to screen for people who pose an increased danger to the university population. They are very sensitive to the effect this may have on minorities so they very rarely bar someone for a non-violent crime.

Another issue is that many programs require licensure by an outside agency, many of which have character or moral requirements. It makes no sense to admit someone if they cannot be licensed. An example would be someone entering an accounting program with a theft conviction.

It's a tough situation for universities since if they admit someone with a violent past and they injury a fellow student, then they are going in severe legal trouble. They have no choice but to exercise due diligence when they admit students. If a university is sensitive to all the issues, and have a very narrow focus, then I suspect things will work out OK.