After an explanation that without L/R crossing the body map in the brain would be flipped upside down, comes this revealing passage:
"To make sense of the sensation [...] your brain would have to switch from one somatotopic map to another one with the opposite z-axis orientation".
This a textbook example of the "Cartesian theater" fallacy. It assumes a little person inside the brain who has to deal with an image projected upside-down. Of course that doesn't make sense.