Now that I've thought about it in the shower, I have two remarks concerning the video procedure.

1. In the beginning of the video, he checks that the square's blade has parallel edges by miking it at several locations. However, he does not make the same check of the body of the square (the bit that sits on the surface plate). Even if the both blade edges turn out to be perpendicular to the plate, the internal angle of the square might not be a true 90 degrees if the inner surface of the body is not parallel to the side that sits on the plate.

2. It's important that the "bridge" bar over the body not move during this procedure. He puts his hand on it while testing but that could lead to movements imperceptible to him. I would rather the bridge were a heavy structure (or suitably weighted) so that gravity would assure it stays fixed and the operator's hands not touch it.