as a mechanic for mini cooper, if they havnt figured it out, i would say take it elsewhere. working on a so called "bmw" is hard but diagnosing fuel or electrical is quite simple.

 

This happened on my 03 Z, turned out to be I got a tank full of water at fill up that day. Clogged up the fuel filter. They did a gas sample and said it was like 25% water. Needless to say that was the first and only time I got gas at that station.

 

We sparyed carb. cleaner all on the valevs and kept on trying to start the car until they just went back to working right.

As I said, this happens sometimes when you rev the engine the turn it off while the RPM still high (not idel)