I would assume the car would not stumble and die if reading was off. The shop says the sensor is throwing 'wierd' signals at 4000 RPM is bull**** did they run the car without it (because they can't) or tap into wiring (doubt it). I don't recall GT1/etc having reading panel for that sensor output.
Either way anything can cause your car to act that way at 4000rpm. So whatever I'm saying here is pretty much a wild guess.
///////////////////////////////////////////// E34 Addicts