The inverter's chassis ground must NOT be wired back to the inverter's neg input! It has to go to the frame on its own. They usually want about #8 AWG for that wire.
Vector inverter manual says the chassis ground is only for reducing RF interference for televisions etc, so no big deal
My Can Tire (I think I already posted this) 1000 PSW inverter chassis ground made a neg path from the shore cord's ground prong (plugged into the inverter) which by-passed my neg path (mostly frame) based battery disconnect switch, so I just did not use the chassis ground and all was well.
Small inverters like my "Source" (was Radio Shack) 400w, that I use now for "whole house" to make the receptacles live, with the shore cord into it, doesn't even have a chassis ground. It has no remote on/off either so I just leave it out front in the cargo bay, "on" all the time. The stand-by drain is tiny and being on solar you don't sweat the small stuff.