Well, learned something new about the travel trailer recently. It is possible to unintentionally fill the fresh water tank and not know it until the tank overflows. Thank goodness for an overflow tube!
After tracing the plumbing lines and thinking through the problem, narrowed it down to water flowing back through the pump. A google search turned up that the Shurflo pump has a built in check valve and others have seen this issue. Since there was 75 gallons of water in the fresh water tank to deal with, why not run the pump for awhile and see what happens. So far that appears to have fixed the problem.
So the Adventure Begins 