I got an electrical engineering degree 15 years ago that I barely use. Although I bought a fairly fancy multimeter, I will freely admit to having only a vague recollection of what I did back then... which was mostly discrete math and signal processing (as opposed to circuits).
A friend of mine who has a lot more real-world "electrician" experience was trying to figure out what was wrong with some cameras he owned. They were powered by cheap wall-warts and failing. We were trying to check these power supplies to make sure they were working, as we didn't know if the problem was with the power or the camera. Sure enough, some of the supplies were dead.
We tried to substitute in some switchable supplies to get them working. In the process, I noted with the multimeter that the polarity was different on the switchable supply from the adapters we were trying to replace. As we were plugging in these 2-prong plugs haphazardly into 3-prong outlets, I wondered out loud if we might have the plugs in upside-down.
He looked at me condescendingly and said "Oh, I see. You have a degree in this, do you?"
Well firstly, it's been 15 years, and secondly...while he may know a lot about being an electrician I know about the diode bridge inside the stupid wall wart. And yes, diodes can tell the difference between electron source and electron sink. But if the power is an AC sine wave then it spends as much time in an up cycle as down cycle and so the decision about polarity is in the circuit post-rectification, etc.
(So it was; to change the polarity on the adapter you just changed the terminals on the plug once it had been converted to DC, not before. Fine.)
But the hypothetical question kept nagging me. Given that one of the terminals is ostensibly true ground, would it be possible to build an AC/DC converter whose DC polarity would flip based on which way you plugged it in (and I'm talking about no connection to 3rd prong)? Do such things exist?