There appears to be some discrepancy on how the towers were actually constructed between {your\percy\my} sources.
Let's look at how relevant it is.
I think we can all agree that the towers were hit by a plane, that the plane caused a massive fireball inside the towers at the floor level of impact, and that there were massive amounts of fuel in the plane at impact (the flights were chosen so that would be the case).
This fuel caused the fireball to be extremely {hotter\fiercer\bigger} than anything that had been considered in the design of the structure.
I think we could also agree that the plane was likely stopped by the central core of elevator shafts and stairwells, so that the fireball would have been pretty well centered even though the impact came from one side.
I think we can also agree that the design of the towers to withstand significant side loads is born out by the virtual lack of any visible sway in the towers when the planes impacted - this impact force was absorbed by the structure -- and that this was a pretty significant load.
Based on this I think we can agree that the tower easily absorbed any tendency to sway during failure because the design stress loads for this failure condition were so much higher than were experienced: the sway was easily contained by the design.
Now we come to the vertical load structure design.
Engineers are loath to spend one dime more on structure than is absolutely necessary once the design conditions are satisfied. They'll consider the different possible modes of failure to see what the structure is likely to need to be able to withstand given normal conditions, and they'll add factors of safety to ensure that the design conditions encompass as many of the possible failure modes as possible, but after that they will minimize any excess possible.
And they will design each floor to meet those requirements. The strength of the bearing components for floor 27 will be less than for floor 26 because they will have 1 less floor to support. The engineers would have taken as much weight out of each floor as possible to keep this structure from becoming impossibly big at the bottom while still keeping within the established design parameters.
I think we can assume that weight bearing strength safety factors were at their minimum, and that the structure was weakest in vertical load.
Wind load would induce a bending load, similar to a cantelevered beam with a constant load along its length, and would increase proportional to the square of the distance from the top (quadratic).
This loading is countered by a whole structure moment of inertia, while weight bearing load is {columnular\compression} load countered by the total cross-sectional area of the support structure. The moment of inertia is made up of increments of cross-sectional area multiplied by the square of the distance from the neutral axis (the center in this case) integrated across the whole structure, so concentrating the windload bearing structure in the steel at the outside perimeter makes sense.
The vertical load bearing strength is just the total cross-sectional area of all the supports - outer shell plus inner core, and it doesn't really matter where it is (as long as it is symetrical). If each floor weighed the same this load would increase proportional to the distance from the top (linear). Each floor would be increasing in weight due to the structure required, so there would be a portion proportional to the square of the distance from the top (quadratic).
So we can comfortably assume that the vertical structure was designed to support the remaining height of the tower above it with some factor of safety, say 2.0 to 3.0 for the sake of the argument.
Now when the structure starts to fail ...
(1) First, lets assume that it starts in the core area on the side with the impact. This area would collapse bringing the upper floor core structure down into the collapsed area and putting all the remaining column bearing load onto the perimeter steel. This would overload the perimeter steel causing a fairly symetrical pattern of failure of the perimeter at that floor. The upper section then crashes into the floor and the impact overloads the structure of the floor below causing it to fail, ibid next floor, ibid all the way to the basement.
Initially the top would appear to fall fairly straight down as this occurs because the initial failure is central and the perimeter contains the swaying loads. The rest of the failure would be floor by floor pancaking in line with the building.
(Impact loads here are much higher than static loads because they have the energy of the falling upper floors as well as the weight.)
(B) Next lets assume that the failure starts in one outside wall or corner. This area would collapse bringing the upper floor side structure down into the collapsed area and putting all the remaining column bearing load onto the remaining perimeter steel and the core area. This would cause an initial asymetrical pattern of failure of the perimeter at that floor at the moment of failure. The center of the impact load of that floor onto the one below would be closer to the center though, because that is where the mass is centered from above. Each floor would then act to bring the center of impact closer to the center of the tower.
Initially the top would appear to fall to one side as this occurs because the initial failure is not central, but then the failure would move to the center as the perimeter contains the swaying loads. The second or third floor may still be asymetric, but the rest of the failure would be floor by floor pancaking in line with the building.
Looking at the videos it appears that the top of the south tower falls to one side at the start of the collapse, and then each floor pancakes, while the north tower seems to fall much more in column, moving slightly to one side as the top section contacts the floor before each lower floor pancakes.
The only way for a vertical concertina collapse to happen - twice - would be from a controlled demolition.
Set at the level of the plane impact and nowhere else, or it doesn't match the observed failure. That they would be able to plan to that level of detail
and be able to coordinate it with people flying the plane that don't know how to land, to say nothing about zeroing in on one specific floor, it is more improbable (imh(sa)o) than a creatortionista ever getting a probability calculation right.
I've spent way to much time on this.
Enjoy.
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