This is weird, and no doubt they are clueless, ...
Fuse F23 is the fuel pump fuse, it is in the front fuse box, and is only energized when the DME asks for it, so hardly can be the culprit unless you have a seized or contacts soldered Fuel Pump relay (in this case, your pump should be about to die on fatigue).
It is easy to hear the pump running (hissing by the right rear wheel) remove the fuse and confirm it is not there anymore. But again, I doubt it is the culprit.
see this thread
http://www.bimmer.info/forum/showthread.php?t=12517
Javier