My fresh water pump, which I replaced a couple of years ago, I know where that is, plus the screen/filter. I've never seen a check valve (if there is one).
I'm not sure I understand the question about the water tank height or if the vent is overflowing water. The way I came across the problem is that my wife kept using the water pump even when the boat was connected to the dockside water. She told me without the pump on, there is very little water coming out of the faucets. With the pump on, its fine. And by using the fresh water tank, it was pretty empty when she told me.
Maybe its the dockside inlet on my boat? Perhaps it has a pressure regulator that isn't working? Not sure though.