I'm sure they appreciate diversity just as much as the next school, it's just that they don't have the privilege of hand-picking the applicants they want because of their locations in poorer neighborhoods (at least in DC this is the case with Howard, as compared to GWU or Georgetown). I'm sure they look specifically for applicants with a committment to underserved/minority populations as well as people willing/wishing to stay in urban areas. I think that matters more than race, personally.
It should be touched on, though, that a lot of this has to do with you and your preferences--your identity as an American, culturally and individually. Do you relate more to white folks or black folks, or do you relate equally to both? Do you prefer to be in a good sized Asian student body for support/cultural interations? You have the right to apply anywhere you think you'll be most comfortable.
There are many other places you could go for the "urban medical experience" if you prefer a larger Asian student community. Even if your stats are so-so, you probably still stand a chance of getting in if you speak about diversity issues and your committment to underserved populations.
You might want to look for the Princeton Review guide to medical schools in your local bookstore or Amazon.com, and check out stats that way. It has the ethnic breakdown of the student body for each school, the average MCATs, average GPAs, etc, etc, etc. There are a few paragraphs about student body, admissions criteria, student life, common complaints and pros/cons from the point of view of the students.
Good luck! 👍