Question about household current grounds from an inverter

I recently replaced a set of two inverters (one 300w pure sine wave & one 1000w square wave) with a single 1000w pure sine wave inverter.

In the old configuration, the inverters were grounded in series. The 300w inverter was grounded to the ground post of the 1000w inverter, and the 1000w inverter was truck chassis grounded.

The power for the two old inverters was wired in parallel. Either unit could fail and the other unit would still have power from the batteries.

The UPS battery backup I used to power my CPAP and Laptop was connected to the 300 watt unit. (Yes, I was a tard. I never paid close attention to the configuration of the inverters. I thought I had a single inverter that was pure sine wave. Smoking a 300 watt pure sine wave inverter is not unexpected when you hook a high power gaming laptop to the circuit it feeds. I'm lucky I didn't smoke the laptop.)

After replacing the old set of inverters (the 300 watt unit lost it's magic smoke.) The UPS started throwing errors and clicking noises with the new 1000 watt pure sine wave unit.

This likely means the UPS is smoked too. Clicking noises normally means dead batteries. I have bought a new unit. I have not installed the new unit yet, until I am certain of the new 1000w inverter.

Now, getting closer to the question... I also bought a standard household grounded outlet tester because I didn't want to cascade smoke more electronics if something was wrong with the install. I got a 'plug bug' which tests grounded 110v AC household circuits. When I plug it into the 1000 watt inverter, it shows a bad ground.

There is a big difference between a vehicle chassis ground, and terrestrial earth grounds. I know this. Is that difference significant enough that a plug bug reading a 110v inverter circuit with a vehicle chassis ground will indicate an error **even if the ground is appropriate for a vehicle chassis ground?**