Ground fault circuit interruptors do trip on ground faults (well, on current imbalances between the hot and the neutral, which is an indirect way of finding a ground fault) and not on overcurrent conditions. Modern units also have circuitry to actively detect continuity between the neutral and ground wires, so they can trip on a neutral to ground fault even if there is no power flowing from the hot to cause an imbalance.
I would also guess that the water heater element is burned out and leaking or partly shorted to ground, quite possibly on the neutral side, which would not cause it to trip the breaker but would create a ground fault regardless of whether it's turned on or not. Shutting off all the breakers in the RV won't stop a neutral to ground fault from causing the GFCI to trip.
While it is true that GFCIs can wear out and become temperamental, it's also very often the case--probably more frequently--that they trip due to an actual ground fault. This is especially the case when the tripping is related to some other action, like turning something on or plugging it in or whatever.
