The water lines are 1/2" PEX. The only things that drain into the gray tanks are 1 1/2" PVC. It seems extremely unlikely that there would be any way for the water line to be connected directly into a gray tank.
Does your rig have washer/dryer prep? Maybe there are washing machine hoses stuffed in the drain.
Also, if you have an outside kitchen, make sure the faucets aren't open.
With the water hose connected to the 4-way valve water inlet, and the valve set to TANK, the fresh tank should fill. If you think it's not filling, you can open the drain valve under the fresh tank to see if water comes out. Some rigs have fresh tanks that hold up to 100 gallons. If the water flow into the rig is limited, it could take a very long time to fill the tank. Cheap pressure regulators can restrict water flow to less than 1 gallon per minute, so it could take a very long time to fill the tank.