i'm sorry but it sounds like you have a kitchen outlet on the "INVERTER"
a converter is a 12v charger
the inverter will NOT do its job if the batteries are disconnected there fore you are on shore power, and have a continuous ground wire circuit thru the shore power cord and transfer switches
but when using inverter mode there IS no earth ground link because the RV is NOT grounded to the shore power system because the transfer switches break that circuit and you are on INTERNAL power not External shore power, so there is NO link for the GFI to detect any leakage, because there is NO leakage when you push the test button, because there is No external ground potential, only battery negative, which is chassis grd
