I hope the photo comes along as I haven't tried this before.
Not long after I brought home our Airstream and was using the black water flush, I also had water running out the belly. This valve was secured tightly to the wall with a clamp. It was the way that it was secured that likely caused it to crack, allowing water to leak down the wall and out the bottom. I replaced it and secured the plumbing so as not to stress the valve body or its connections.
The way the valve works; water pressure forces the piston up against gravity, this applies water pressure to a spring loaded ball valve. The water pressure overcomes the spring pressure and water flows past the ball to the spray head mounted near the top of the BW tank (somewhere). The design of this valve is supposed to prevent the possibility of back flow.
On my '08 27FB, this is located under the closet accessible through the access panel. Location may vary depending on model, the location of the original leak may give you a clue as to it's approximate location. I would inspect it to see if it is still good. If the spray head in the tank is plugged this might be a difficult task.
I've never tried to fill the BW tank this way, but use it to introduce additional water before dumping and also have left it on for several minutes with the dump valve open until the drain hose ran clear. I have used it to add water to the tank before a weekend trip. Running it about 3 minutes fills the tank about 1/4 full. This is definitely not something you want to leave running with the dump valve closed for any length of time (getting distracted, etc.) or you might get a part in the sequel to Robin Williams' RV movie.
I agree that it's spray pattern may not be very effective at rinsing the tank, but it is a convenient way to add water to the tank when flushing; and I often use a couple of fill/dump cycles using it to add water to the BW tank