There is one situation where Junior Electrician may have a point. Your water leak (dump) tripped the 120 volt GFCI, but your furnace also failed to function. The furnace is 12 volt, but the Converter supplies the 12 volts when connected to shore power. It's not out of the question that the entire converter went into a protection mode. If they overheat, they will simply shut down and then restart after a cool-down period. They may also have some sort of automated protection circuit if they detect a ground fault type of current leakage in the 12 volt circuit. I don't know of one, but anything's possible.
This is the online manual for a 2015 PUP. This section covers the converter.
Forest River Manuals
It doesn't quite say that pulling the plug from shore power is a remedy, but if water somehow followed the 12 volt wire to the furnace or the thermostat, "something" may have tripped in the converter and since you then pulled the plug to take it home, whatever tripped may have reset after pulling the plug.
That's a whole lot of imaginative, magical thinking regarding the 12-volt circuits in the camper, but it's not entirely out of the question.
As for the GFCI's, FlyBob is right that there may be more than one in your camper, and in that case, either one could be "upstream" of the 120 Volt load(s) that stopped functioning. A GFCI outlet is first in line between the panel and additional outlets that are also protected by that GFCI. Often 2 or 3 more outlets can be downstream of the GFCI depending on the size of the wire and electrical code.
GFCIs confound lots of people.
It's kind of sad that the wires passing under the sink are not "dressed" and routed in a way to shed water. Assuming that the wire jackets are not damaged, water on the wire itself will not trip a GFCI. Instead, the water traces along the wire until it enters a device, like an outlet box, and then triggers the GFCI by contacting a screw or bare section of wire where it connects to the GFCI (or other) outlet. The water creates a kind of bad circuit with a trickle of current flowing between the hot (black) and bare (safety ground). In a valid circuit, current should only flow through the black and white wires. The third (bare) wire should have no current flowing through it.
I had a farm, and I literally ran extension cords from GFCIs through the water in a pond. So long as the jacket on the wire was intact, the GFCI would not trip. In fact, I could plug a submersible pump into the extension cord, tape up the connection really well, and submerge the plug!
The same should be true under your sink. You could address this by slightly adjusting the wire routing to be "uphill" as it moves "away" from the sink, or by adding a "dam" of some sort to the wire. The dam might be a rubber grommet clamped around the wire and then sealed with caulk. Water following the wire would hit the "dam" and drip off the wire rather than continue to follow it to a device. Of course, your sink shouldn't leak, and everything with water leaks now and again. But even household kitchen sinks have electrical connections to garbage disposals, and so on. Proper wire routing involves creating a "belly" in the wire so that water following the wire will reach the bottom of the belly and drip off, because it can't follow the wire as it turns "uphill."
Anyway, the precautions for ensuring your drain won't come apart again are step 1 in never having this experience again.
And that Gorilla tape belongs in the camper, too. 
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