I don't know about you, but if I turn a picture-postcard around its vertical axis, left-to-right, all I see is the blank back of the picture. (Likewise if I rotate it around it's horizontal axis.)
What you're actually saying is if I put the picture on transparent acetate (or whatever) and rotate it, then look at it through its back, I see the same as I would in the mirror. Which is essentially the same as reversing the depth of the object (when you think about it.)
And there's nothing privileged about the Left-to-right rotation. When you face the mirror and hold the picture up (facing the mirror, away from you), you chose to rotate it around its vertical axis to face the mirror (thus swapping left and right). If you chose to rotate it around its vertical axis, top-to-bottom, to face the mirror and away from you then you get the other situation.
What you're actually saying is if I put the picture on transparent acetate (or whatever) and rotate it, then look at it through its back, I see the same as I would in the mirror. Which is essentially the same as reversing the depth of the object (when you think about it.)
And there's nothing privileged about the Left-to-right rotation. When you face the mirror and hold the picture up (facing the mirror, away from you), you chose to rotate it around its vertical axis to face the mirror (thus swapping left and right). If you chose to rotate it around its vertical axis, top-to-bottom, to face the mirror and away from you then you get the other situation.