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Because within the cube, the centerpieces are fixed to a core. And because these define the orientation of the cube and are fixed within the robot you end up having the same orientation every time. This happens with every solving robot that only turns the outer layers of the cube, meaning the inner layers and therefore the centerpieces do not move.

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Does that imply that when they remove the cube (note that it is not permanently fixed to the machine), manually twist it (i.e. to shuffle to a random state, as in the video), and replace it, it has to be returned to a certain orientation?

Again, it still solved to the same final colors orientation even after it was removed, hand-shuffled, and replaced.

My apologies if I'm seeing something that isn't there.

It's mathematically interesting that the optimal solutions (I assume that the robot uses the fewest-moves-possible to get its high-speed results) never require rotating the middle layers.

On closer look it's actually trivial. Any move that requires rotating a middle layer is isomorphic to rotating the top and bottom layers in the other direction. :)

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