That isn't an automatic. It depends on the strength of the structure below.
There is no such thing as "the strength of the structure below".
There exist the strengths of individual components & assemblies, which will have innumerable & wildly variable values depending on how that component or assembly is loaded & supported.
The strength of any component alone is irrelevant. The ratio of the INDIVIDUAL (not average) DYNAMIC (not static) stresses to the strength of each individual component tells whether or not that component will survive.
Calculating "individual stresses" means that you have to know which elements contacted which in the upper & lower blocks.
Calculating "dynamic stresses" means that you need to know both the local & global stiffnesses of both the upper & lower components as they exist in the DISASSEMBLING (not "as built") building at the moment of the individual collisions.
Chaos renders either calculation impossible in something as complex as the WTC towers or WTC7, except
perhaps for the first colliding floors. So you have to take a statistical approach, and recognize that your results are merely indicative, rather than deterministic.
In reality, collapse propagation is a collision event, and should be analyzed (if one is going to bother to attempt to do a calculation so fraught with uncertainties) using the same impulse-momentum curves that were used to model the impact of the planes into the towers.
The difficulties in this analysis are the same as above, which appears in calculation of the reference curves on that diagram.
In doing so, one would find out that one was sliding around the curves from low to high impulse rapidly as the upper block gained momentum.
If you are following this issue much at all you would know there have been failed controlled demolitions. Some of these failures can be seen on the Internet. Why did they fail?
Why don't you attempt an answer of your own question.
It is patently obvious why those demolitions failed.
And it is patently obvious why the conditions that permitted those failures could not possibly arise in either the towers or WTC7 collapse.
And it is also obvious that "the strength of the structure below" played zero role in the survival of the building in the vast majority of the failed-demo cases, because the only "structure below" was the ground.
I'd be very surprised if there were not already a thread on the failed demolitions...