The school exists to educate physicians who will ultimately practice in central or southern Illinois. The best way to ensure this is to accept students with strong ties to that area. It works. UIC-Peoria actually started as the Peoria School of Medicine to education downstate physicians, but once they affiliated with UIC and started accepting students from all over the country, a very low percentage of applicants stayed to practice.
Anyway, if you did plan to practice in central/southern IL then maybe you could apply and state that somewhere in your application. However, choosing to attend college in Chicago doesn't make it seem like you would have any reason to practice downstate. This is no different from the University of Mississippi not accepting OOS residents. Illinois just happens to be a large state with a diverse population that either clusters around Chicago or lives farther out. Also keep in mind that UIC is the largest medical school in the country, with multiple campuses and a 300 student entering class. So IL residents still have a very solid chance at another state school. SIU is just 72 students per class. Rush and Loyola also happen to have a very high percentage of IL residents per class. Try to see the big picture and not get discouraged.