The separate chassis ground from the inverter is for safety in the event that the inverter case becomes energized in a fault situation. It has nothing to do with the circuitry of the inverters operation, hence, it can not create any type of ground loop. Any power to the separate inverter ground wire will only occur if the inverter fails and something internal connects to the case of the inverter. In that limited possibility, the ground is connected to the vehicle chassis and anyone or anything in contact with the inverter case will not be harmed.
That ground connection is for safety and should be connected to the vehicle frame, not to the battery (-) phase. In the event that the inverter case is energized it may pass 120V to the ground wire and that could lead to other problems with anything connected to the 12V system or the battery, should anyone choose to connect the inverter case ground to the 12v battery ground,
I'd suggest to follow the Mfg's instructions and connect that separate ground wire to the frame of your RV. If you get an 8 gauge wire with an
insulated ring terminal, it is an easy operation to use a
self tapping screw through the new ground ring terminal and into the frame.
Good luck with your inverter installation and the ground. FWIW, I have the same inverter and believe it's a wonderful product. I use mine to power a residential fridge and 120V entertainment gear. It handles everything well. I've never heard the fan come on while in use.
