It has do to with how one visualizes the structural behavior of perimeter. You can do it in any of several ways, and each way sets up a different expectation for how the building collapse should look.
Imagine one of those lightweight plastic structural grids like you often see as part of trade-show booths. Now imagine a large sheet of paper attached to the front of a fairly broad expanse of it. Think of the paper attached by little rolled up loops of tape joining the paper to the grid at various points, just enough to hold it up and keep it flat.
Now go in and judiciously cut enough of the plastic grid pieces so that half the structure supporting your facade collapses while the other half stays standing. What happens to the paper? You might be able to imagine several things. The paper might tear, in which case the portion that was connected to the failed structure will fall with it, leaving the other part still attached to the still-standing structure. Or the failing structure might pull the whole sheet of paper away, severing the connections between the paper and the still-standing structure. Or at the opposite extreme, the failing structure may tear its little tape wads away, leaving the paper intact, still stuck eccentrically to the surviving structure, and roughly in its previous shape, if otherwise crinkled and now waving in the breeze.
The Truther proposition seems to be a scenario along the lines of the first two, where the perimeter should fail in a way that reveals any asymmetric nature of interior failure. The debunker proposition is more like the latter, where the perimeter stays intact but deformed and poorly supported. To understand how those can legitimately differ, imagine the thickness of the paper in the scenario varying between tissue paper and cardstock. Those are kinds of paper that would have different mechanical properties in this toy example. The tissue paper would be less likely to stay in place and more likely to follow the falling plastic grid. The cardstock would be more apt to hold its shape and stay in place even if much of the structure behind it had failed.
So I think it may be fair to say that the expectations regarding the perimeter wall vary according to how people intuitively envision the specific strength of the wall itself.