There is no ground loop because the neutral-ground bond is in just one place, the inverter. No other neutral-ground bond should exist. Any bond at an onboard generator would be broken with the transfer switch same as the inverter when not in use.
The ground is for internal failure on either the 120v or 12v side. Needs to be direct to the frame so that no matter what fuses or switches you have on either side the inverter chassis remains connected to the frame in all conditions. This makes the inverter chassis just a safe as touching the frame. Ungrounded electrical equipment leaves open the possibility that YOU become the ground.
Go down to Home Depot and get some #8 green wire and make the connection.
