I wonder if they have active systems on board to monitor clearance, or if they depend on the river monitoring systems.
I was on the upper deck of the Carnival Destiny when it passed under the Verrazano Narrows Bridge leaving NY. There seemed only inches to spare that time too. In fact, it looked like it was certainly going to hit the bridge, and then magically passed under it. I learned later that somehow when the ship moves faster, it draws itself down into the water and that can be calculated precisely.