I had a similar problem, only it was because the windshield replacement company wasn't very professional.
Using my Insurance company's repair shop to install the replacement windshield was easy. It was three blocks away. When I picked the rig up after the service was completed, I drove it around the circle of our town. $ lanes, 55 mph in places, and everything seemed fine.
Our first trip with the new glass, I didn't make it out of town, and the passenger side trim did the exact thing you described. Sounded just like a loud "jake brake."
The worst thing was that the repair facility did not reinstall the trim properly, lost one screw, replaced it with a shorter screw, and then covered the head of the screw with the black urethane to hide the fact that they put a different type screw.
The replacement screw was too short, so the tech added more urethane to the back side of the trim piece to hold the screw in place, and give the appearance that the screw was in properly.
Oh yeah, it was raining when this came apart, and I was in a parking lot on a ladder, in the rain. Luckily, I keep some hardware on-board, and had a perfect replacement sized screw for the ones that wallowed out while flapping in the breeze.