If this was a projector, there would be a menu option to flip, as if it were installed hanging from a ceiling, but I found nothing, and ended up calling Samsung support. 30 minutes later, with them having a very hard time getting them to understand "upside down", they told me to take it back to Fry's or schedule a service appointment. Waiting for an appointment was absurd, and if I could fix it without taking it back life would be simpler.
Some Googling looking for Samsung TV service menu found a site with codes for different models. In this case, the magic was, turn the TV off, then "Menu - 1 - 8 - 2 - Power"
Which takes us to an upside down service menu. If you don't get it when power comes on, you didn't hit the keys fast enough, so turn it off and try again.
With your head tilted enough to read, select the "Options" menu.
Then the "MRT Options"
And "HV Flip"
and use left-right arrow keys to turn it from whatever it is to the other way, in my case, "off" to "on".
The results are gratifyingly immediate.
Turn it off and back on, and it will stay that way until a "factory reset" is done.
I didn't find a page that cleanly addressed this, so here it is for anyone else.
What's actually wrong? To see if it had an attitude sensor like a phone or tablet, I turned if off and flipped it physically upside down and turned it back on -- no difference. I'd guess there is something that was plugged in backwards during assembly, an example of the very phenomenon that led to formulation of Murphy's Law - a unkeyed connector, or one that was mis-wired.
It might have helped talking to Support if I'd know the magic term in the service menu was "HV Flip".
Samsung UN28H4000BFXZA
Blood cost: none!
