[GregoryK]

I can't comment on the M2. Mine does not have this problem...yet. But DMF's can be problematic. They are really good at stopping noise and vibration from entering the vehicles interior. Having driven standard cars all my life I was surprised when the clutch on my MINI Cooper S was slipping at 8,000 miles. BMW Canada would initially not replace it under warranty but eventually folded after I pulled a few strings. At the time the head mechanic told me that just one heavy slip of the clutch was all it took with a DMF. After you had done that it was only a matter of time before the clutch would fail completely in a MINI. In my experience a regular clutches can take years of abuse where a DMF clutch is way more temperamental.
From the OP's description this sounds like what I have experienced. Because the clutch and flywheel have a "burn" mark on them they start to "chatter" slightly when hot. It would be interesting to have seen the clutch and flywheel that they took for the car. I really doubt that piece of paper would have caused the vibration but may have been enough to start another problem.