I think they baited you with their "loook, movement" replacement videos. As far as I can tell, their inputs have a fixed background and are of constant exposure and camera position.

No, the camera is indeed allowed to change a tiny bit. For example, you do not need a tripod. Taking photos with a handheld camera works fine (although a tripod works even better). They explain it in greater detail in their paper: https://arxiv.org/pdf/2004.00626.pdf

Background subtraction methods on the other hand usually fail if the camera moves even a tiny bit or the lighting changes slightly. More advanced methods can recover eventually, but you still get a few frames with improperly removed background.

In the first example (the one with the girl), you can see that there are small camera movements. You can also see the effect this have when applying straightforward background subtraction in the second video.