You are lucky that you "only feel crappy" rather than "wear crappy"
The black water system is a "closed" system EXCEPT for the dump valve, the toilet valve and the vent stack. With the dump valve closed and the toilet valve closed, when you add water through the flush port, once the "closed tank" is full, the only place for the water to start flowing is out the roof vent stack. Had your holding tank been "somewhat full of poo" that's what would have been flowing onto your roof (sort of "wearing crap").
Thankfully, all your plumbing on the black tank seems to have been "properly assembled and glued in place" at the factory. Occasionally a vent stack or a toilet port are not glued to the tank and the water pressure from a full tank can push the parts away from each other causing a "nasty leak" that will flow out the bottom of the RV. In your case, the components held as they were intended to do and the water (complete with poo) started flowing up the vent stack and out onto the roof.
Luckily, from your description, the tank was at least "somewhat clean" or you would have had a mess (literally) to clean up
