If there is one thing to learn from this forum, it is to NEVER assume a used RV has not been modified by the previous owner. In fact, if THESE RVers are any indication, it would be safe to assume the opposite to be true.
Really, there should be nothing going intothe black tank that doesn't go down the toilet. One exception is the tank flush port. My coach has a dedicated port, not connected to the fresh water system, that I have to connect a hose to. Its right next to the city water inlet, so make sure your city water is connected to the right inlet. Previous owner may have plumbed that black tank flush port to the fresh water system, check that.
The previous owner may have installed a tank balance mechanism to move grey water to the black tank. Some folks do this to maximize holding capacity and thereby lengthen the time between dumps. Most often I hear of them using a separate pump for that, but I suppose it could be a gravity system if the tanks are positioned to allow it.
You might be able to turn off the water at the toilet to eliminate it as the source.