In my mind Regula One WAS upside down. We saw how the station was oriented at the beginning of TMP when Scotty and Kirk left in the travel pod. No reason for the entire station to be inverted and no reason the transporter couldn't compensate for the difference in orientation.
Meh, ships should not be designed with bilateral symmetry either. There is only one axis which matters in space (forward/back). It makes sense for a ship to have a front end and a back end, but not to have a top or bottom or dedicated left and right hand side.