Any structural member has a front, a back and two sides, and when it flexes the front goes into tension and the back into compression. That's the mechanism by which an elastic solid resists flexure. Flexing a structural member stores potential energy in it, however little it flexes, and as long as it hasn't reached the elastic limit that energy is available as kinetic energy when the stress is removed. Therefore, there is no such concept as "not enough to store potential energy for springing".
So a box column can't flex, but a much bigger compound box column can? This is absurd. If the whole building flexes, then the columns have to flex. As for the building having "tremendous strength and considerable flexibility- just not to the point of the box columns kinking though", what is this actually supposed to mean? The strength of the building is a measure of how much it can resist a deforming force without permanent deformation; in other words, it's a measure of how far it is to the point of the box columns kinking.
Do you have even the vaguest idea what you're talking about?
Dave