For use in the RV, you generally should be switching the neutral as well as the ground, whereas a standard residentail backup generator installation does not require that.
The details can get a bit complicated, but basically neutral and ground should be bonded together at exactly one point near the power source. For a house, that one point is the main circuit breaker box. For an RV, when it's plugged into a shore power receptacle, that one point is the main breaker box supplying power to the receptacle that the RV is plugged into; but when operating from a (built-in) generator, neutral and ground ought to be bonded together at the generator. The way to accomplish this is to switch the neutral as well as the hot.
I'm guessing possibly inverter is sensing that neutral is bonded to ground and based on that refusing to turn on. I could be all wrong with that guess. Regardless, there are good reasons to want to switch both the neutral and hot leads in an RV transfer switch (not only because the electric code demands it); in certain fault conditions, it helps avoid damage to equipment and/or danger to people.