If the rig was winterized, the water heater was drained of water and then bypassed. The water from the campground spigot or from the water pump may just be going around the water heater. If you've had the electric heating element turned on with the water heater bypassed, the element may have burned out, requiring replacement.
While hooked up to campground water, open the Temperature/Pressure Relief Valve on the outside of the water heater to see if any water comes out. In the photo from the prior post, it's the thing near the top. Use a pair of pliers as the water coming out could be hot.