Maybe you might wanna go to Leipzig instead. Longer runways, less traffic, hospitals around and AF regional offices.
Within 5 min by car from Tegel Airport there are two major hospitals (Virchow+DRK) well equipped for emergencies. Landing in Leipzig you have a 20-30 min drive to the university hospital. So for the passenger Berlin was a better option. Also while Berlin is a densely populated city, except for the last app. 8 nm of approach to Tegel from both sides you fly over mostly woods and farmland.
Because of the proximity of good hospitals, Tegel is probably one of the best airports worldwide for medical diversions if you don't have a specialized helicopter in standby.