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The MB service manger sat in the back while I drove around the block. He immediately identified the source of the problem- a loose tab on the headliner. He demonstrated the noise with just one finger pushing against it. Just got my car back from the MB two days later.
I got the car back from the dealer - they fixed the rear bumper issue (plastic pieces between two panels were touching; resulting noise) - they refitted the bumper and placed isolating material in places two pieces could touch.
Roof/door rattle gone - they opened the rear right door panel, replaced the "fixings" (had to leave the car overnight because these "fixings" needed to be ordered from the MB). They told that new "fixings" are harder, they fix the panel better and do not allow it to move.
After a long test-drive one conclusion - this fixed my problem. Let's hope the rattle stays away.
Mine was the very back of the headliner - tab was not secured / loose. I didn't bother to have them fix it coz I didn't hear any rattles from the headliner.