I would guess that the neutral and "ground" are not bonded by the inverter.
It's possible that you could fiddle with e.g. the transfer switch setup for the inverter to bond them when using the inverter (and only when using the inverter). However, it's also at least theoretically possible that the inverter would not work with its neutral output bonded to ground with some output circuit designs. You'd have to consult the inverter maker.
I personally wouldn't worry too much about the light. My guess is that in practice either they would cover any reasonable fault under warranty and have the disclaimer for the odd situation where the building wiring is dangerously faulty, or else they would try to avoid warranty coverage for using the UPS with an inverter in the first place, apparent wiring fault or not.