I know 2 young people who have made careers in the US Foreign Service. Neither went to college in DC. (One graduated from UOklahoma–which is about as far away from DC as you can get.) The commonality-- a high level of fluency in a critical foreign languages (Russian, in both their cases ) plus substantial experience living overseas in in Russia or former Soviet Union countries.
I can assure you that UM’s hospital is right on campus. Plus there is a campus shuttle service which has several stops at UM hospital & medical buildings. (D2 spent 2 years working at UM’s med school before she started med school. She used to ride the shuttle/city bus every day to work. She got dropped off right in front of the one of the hospital entrances.) Her BF was doing his PhD in bio and all the bio buildings are right across the street from the hospital. So is one of UM’s dining halls. The hospital isn’t on the central campus, but the medical buildings are an awful lot closer to central campus than the north campus and many of the dorms are.