You don't support this statement.
I fear that you are modeling the entire tower as a single column with a heavy load attached at the top (mushroom), when the model and method used to construct WTC 1 and WTC 2 was a three dimensional lattice. NIST describes the benefits of this design as allowing for more rentable area (fewer required vertical members) as it distributed about a fifth of the load bearing into the floor supports.
Except in the set of floors (from the pictures, it appeared to my eye that between three and six floors were directly influenced by the impact) where impact occurred, load distribution could be expected to perform as designed. In the damaged floors, loads were still distributed horizontally somewhat, though in a degraded lattice, which led to floor sag, failures, and some photographs indicate the internal buckling of vertical members associated with the forces from the floor.
For the top to fall off or topple, a significant number of vertical members would have to fail under tension, not in torsion. It doesn't appear that the loads (based on the tilt angles I have seen in various photographs) in the upward direction were sufficient to cause this mass failure (partly due to load distribution via the lattice) before the sag and buckling combination induced the failure in torsion and compression, leading to the "buckling" failure referred to in the OP.
For simplicity, it might be more productive to argue material science in one point, and separately describe why the toppling "should" have occurred.
DR