"Why would pressure coming back on in the park cause the pump to run the tank dry?"
This doesn't directly cause the pump to come on and run the tank dry. If the pump were left on after the park water comes back on, when you run a sink or shower, the pump will come on and draw its water from the tank. When the tank eventually runs dry, the pump runs dry. This is not good for the pump as it will continue to run because it can't build water pressure with no water in the tank and run till it burns out.
2003 Sightseer 30B riding on a P-32