I came home last night to find several things.
1) The mother was only slightly exaggerating.
2) The water heater was fine.
3) There were no leaks in the walls.
This pointed the finger in one direction: the sink and the overflow pipe! Touched the end and found it wet. Ta-dah. Luckily, more than half of the water that had been backing up in the drain had rolled directly into the sump pump hole. I bailed out quite a bit of it and turned to the handy dandy Shop Vac to get the rest.
I found with disgust that our ginormous ShopVac that I'd bought last year, apparently came WITHOUT a foam sleeve for water pick-up. WTF?
I swabbed and scrubbed the floor and set up the dehumidifier. On today's list of things to do is to buy the missing foam sleeve and suck out the remaining water. Then I can clean the cache hole and this chapter will be closed.