it was mostly a joke, since the right-hand rule is itself an arbitrary convention.

I think you are right though; "up" and "down" are defined by applying the right-hand rule to the orbits of the planets around the sun, not their rotation about their own axes. this is why we consider venus to spin "backwards" as opposed to being "upside down". this does lead to an odd conundrum in the case of uranus, whose axial tilt is almost a right angle. which of uranus's poles is north?