The real culprit
I have experienced skyscraper sway, being extra-sensitive to it. Sway is handled by visco-elastic dampers. Without them, these buildings would have to be 10 times strongers so that they can stand up to the wind. The WTC towers had thousands of such dampers between the beams and the concrete. In other words, everything was glued together using 3M material and these products from the late 60s were not exactly state-of-the-art - and the WTC was the first use of them due to its sheer walls and wind loads.
The visco-elastic dampers melted under the heat, producing live loads. No one wants to mention them because a lot of skyscrapers would have to be torn down were that the case. Look it up
How visco-elastic dampers failed