Well I am thinking of the plane as a 2 D plane. If a child shows you a drawing and you tell him to try looking at it upside down, I think only the very rare child would turn the drawing over and look at the back. If I show my friend a photo with unclear gravity and he orients it bottom up and I tell him he is looking at it upside down, he would be a joker to turn it over and look at the back of the print and say, Ah you are right it does look better.
To me upside down is to spin a flat object around and look at it upside down. If you were to take a famous flower painting to a dealer and have it upside down you would have it like drawing number 3. IF it was instead like drawing number 2, when the dealer turned it round the right way he would exclaim "But it is backwards! It must be fake"
So that I think is how my head sees upside down. Now if you are talking about turning a coffee cup upside down that is a different matter. Or if my wife says I would prefer you have me upside down tonight honey I would be confused. You mean like yen yang or like canines?