Well, like the name says, the MID displays information only, it doesn't compute the information displayed there. So, without a MID or with a broken MID for example, you can still connect to, diagnose and even code the car. However, I guess I am missing something out here, since the car was inspected by a master engineer at the dealership and this is what they came up with. As a last resort, you could indulge them and temporary bring them a MID from a friend with another E53.
There always is the all-around solution for the BMW electrical issues - disconnect the battery for a couple of minutes