Of course what really happened was that the top portion did collapse more on one side than the other, but then that part fell more or less straight down, canted over, as the floors below it pancaked. The upper floors, in both towers, were not destroyed during the collapse, but rather when they reached bottom.
The other day, there was a show on the WTC collapse - Nova, I think. Included interviews with Leslie Robertson, structural engineer for the WTC. Blamed at first, he was vindicated. Robertson now is working on the 1600+ ft World Financial Center in Shanghai.