I think "reflect top to bottom" is intended to mean "swap top and button". A mirror reflects left, right, top and bottom perfectly.
It's front and back that it swaps.
Someone saying that a mirror swaps left and right is comparing it to a photograph, and only because we, as bipedal creatures, really prefer to orient images of other humans with heads up.
Someone saying that a mirror swaps left and right is comparing it to a photograph, and only because we, as bipedal creatures, really prefer to orient images of other humans with heads up.