It is not a good thing to put the coffee basket back in place without a filter of any kind inside it.
It is a good thing that the coffeemaker sits in a tray with sides. That confined the area that had to be dealt with. It seems that the wet grounds slowed the rate of flow through the bottom of the basket. Water flowed over the top, carrying some of the grounds with it. And some of the grounds passed into the carafe, as well.
This morning, I'm pouring my cups of coffee through a fine mesh strainer so I don't have to strain the grounds out with my teeth.
The upside? We now have a super-clean coffeemaker.