I assume that we're talking about a 12vdc->120vac inverter. and would be a SDS in this environment. So when the RV is on it's own and the inverter is supplying 120vac to the RV's internal wiring, it does need a N-G bond (for a fault current path). However, when external power is supplying the RV's internal wiring, that bond must not be in the RV. (It's in the service supplying the receptical that the RV's plugged in to.) Note- the inverter's equipment ground should be connected to all the other equipment grounds & to the chassis.
Without looking at things, I suspect that there's a single-pole transfer switch somewhere in the circuit where there should be a two-pole switch.
(I've seen a few 'home-wired' RVs with nice QO load centers and a solidly-mounted (and bonded) ground bar.)