Fresh water tank magically fills itself

It's worth noting that when the built-in check valve in the pump fails, there is no way to "check it", really. You could pull the pump apart and examine the diaphragm for debris. You can usually buy replacement diaphragms for the pump, or just replace the entire pump. But the check valve is part of the diaphragm design. I wouldnt add an additional check valve in-line, as it is just a matter of time where the pump stops pumping all together.