I did some testing on this yesterday.

I'm beginning to also think that it's the tranny. You hit the gas and it searches for a gear. You'd think that an "advanced BMW computer" could find 1st gear, but what do I know..... I think that this is where the hesitation comes from. If you go to manual mode and force it into 1st, it goes immediately. In auto mode, it seems like the engine is revving but no power is sent to the wheels for a split second. I know diesel's struggle from a standing start without the turbo, but I cant fathom it having NO power while the turbo spools up. Stabbing the gas eliminates the hesitation that a light foot brings, so maybe the tranny can figure it out in that situation.