Alrighty. Weird stuff. I reinstalled, but it didn't really help. I think.
I've been testing in single player with the pre-made characters and the demo scenarios. I tried the House of Doors demo, and hit the Print Screen key seven times. Then I moved around a little so it would be easier to distinguish the shots, remapped the key to Print Screen to sorta reset it, and hit it seven more times. Then I exited to the menu and started the Cat Lady one with the same character and did the same thing as before. Then I exited the game and checked the screenshot folder.
There were ten new screenshots. Not twenty-eight like there should have been, not none like before, but ten. Those ten were a mix of the fourteen shots taken in the House of Doors demo, some before the move and some after. There were no screenshots at all from the Cat Lady demo.
I have no idea what's going on. I may make one of those possibilities my own and retaliate after all.
[Later...]
Everyone take note: That is apparently an awesome, effective, MAGICAL threat. Use as necessary. Screenshots seem to be working normally now, despite doing nothing but threatening textually to retaliate. I am tempted to take bets on how long this proper functioning will last, though...