My guess... :-)
I'm betting it has something to do with the fact that the cube has a history state once immediately created,
but when you alter the cube, it becomes a joined/multi-surface object and does not have the ability to alter its sub-surfaces by moving any points. In fact, the points shouldn't move if adjoined by multiple joined surfaces.
You could use the Twist command, but that would make a smoothly transitioning twist. If it's a simple structure you might have to resort to using a lot of construction guides.
What would work here would be some kind of "cage" manipulation, not available yet.
Further experimentation shows that you are only able to edit structures, namely cubes, based on planes where there are no trim curves present.
The surfaces in the structure can only be four-point planes. You can Extrude a Plane, by the way, (not a trimmed plane) and manipulate its points as well.
Once you add any other complex surfaces like Fillets, then you now have compound and trimmed surfaces joined together and that cannot be simply manipulated by moving corner points.
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