The lower section can exert an eccentric reaction force on impacting debris and freestanding components. As SanderO mentioned, the perimeters peeled away in large sheets and fell outward. This is just like anything tipping over; there's an initial bias towards one direction for whatever reason, then gravity drives the fall with the fulcrum and material providing horizontal reaction force to displace the center of mass of that component away from the footprint.
Even if the towers collapsed entirely straight down, the debris would still assume an
angle of repose characteristic of the materials.
What Menard_K expressed, though, was surprise that the collapse could continue while it should be losing "so much" mass outside the footprint. This is incredulity over an unevaluated (by Menard_K) condition. First, what is the
theoretical effect of mass shedding on existing models? Second, what are the
real circumstances surround mass loss to outside the footprint in the tower collapses?
As far as models go, the various 1D models are really all there are. The best FEA models of tower collapses - and I only know of two, neither of which are full tower replicas - do not offer anything over the 1D models, if as much. These models indicate that fairly high mass loss can be tolerated throughout a continuing collapse, and moderate amounts like 10% don't greatly affect the results.
For the real collapses, two categories of components can be directly seen to have not participated in
driving the collapse: the peeling perimeters and core remnants. The perimeters fall over
after an interior collapse front has already passed by, stripping the floor slabs and removing critical lateral support. It is
because the collapse propagated without the involvement of the perimeters that the perimeters fell. Likewise the core remnants, though lateral support was not so much an issue for the wider surviving remnants; lateral debris pressure at the base likely was. So, as far as reality goes, these masses did not drive the collapses, but neither did the structural capacity of these components contribute to resistive force. Lack of "participation" goes both ways - mass not driving, capacity not resisting.
Up to this point, the narrative I offer doesn't indicate a preference for natural collapse or CD. There could've been a cascading interior collapse due to damage plus fire, or there could've been charges to separate one or more slabs to get it going and possibly keep it going. Regardless, the mechanics of an
interior collapse through the floor area is what needs to be considered, as this is what's observed (it's not necessary to infer that aspect when expulsions are seen passing an area and considerably later the perimeter falls away).
With regards to an interior collapse, the core and perimeter act as temporary "retaining walls" to prevent mass loss from an interior collapse.