I think a separate case ground is used on some inverters so that if the 12v negative is not present and the inverter fails, creating a short to the case, a ground is present to protect the user and connected parts. I have my inverter mounted on an aluminum plate so if the inverter case was energized, the mounting plate could also serve as a ground plane, something I wish to avoid. For the Xantrex SW1000, I used a separate AWG 8 to frame ground point.
As BFL has said, the tester may show no bond between neutral and ground for 120v receptacles and be correct.
