My guess is your black tank has a "slip fit" on the top with gasket..
HOPEFULLY - You just need to drop the underbelly and allow EVERYTHING to completely dry out.. Possibly replace insulation if there is any... Once insulation is removed, give the underbelly a good spray of disinfectant before closing up.
This happened to me but it was not from a hose left turned on.. I Used to ( ROOKIE MISTAKE ) keep my black tank flush hose hooked to the trailer with the shut off valve closed the night before leaving. my valve failed and slowly filled the tank to the point of overfilling and spillage into the underbelly.