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Shouldn't the inverter be passing the EGC through to the negative terminal of the battery hookup, grounded to the car frame?

Another thing to consider would be 250.114(3)b.

What Tesla said but not as detailed.
Isolated grounds were required back in the day to address the problems of noise on the bonding wires being interpreted by the computers as data. Computers have much better power supplies today but bad bonding and grounding still creates data errors.
Tesla Gives about the best explanation I have read and I think this time I even understood it.
The idea that the ground does not need to follow the circuit conductors might work fine for the data but the circuit breaker likes the ground to follow the supply wires to reduce the fault impedance.

No, an inverter (at least the small consumer models) has no connection to the ground pin. On a PC it will be hovering around 60v above and below the neutral and hot because of the noise filter in the PS.
I ran a jumper directly from the PC power supply can to the car frame to fix the hum. That made DC ground in the PC the same as ground in the car. Prior to that the ground connection was through the shield of audio signal cable (which is also a signal path).

As for IG, it seemed like a good idea but IBM abandoned the recommendation in the late 70s as being a waste of money.
Most of the noise was coming from our switch mode power supplies in the first place. They fixed the PS problems and the noise problem pretty much went away. The use of CMOS instead of TTL also made machines a lot more noise tolerant. They also lost their obsession with "ground loops" about that time and we stopped doing all the base plate ground checks insuring the holy grail of a single point ground. For the last 30 years multiple grounding points in computers became the norm, using the logic that creating a ground plane was better than striving to have "star wired grounds". Look at a PC interface sometime. Every one of those D shell connectors grounds through the shield of the cable. When we had transient problems we added bonding, which by definition is a ground loop. Just like 250.6 says, we did try to avoid signals on or referenced to, the ground tho. That is why you see so many differential interfaces like Ethernet, Twinax or Token Ring. The newer machines even went to a differential SCSI interface.
It is duly noted that the only damage I have ever seen on my PC was a lightning hit to the weather station mast and it broke a single ended serial port interface.

Unfortunately old legends die hard and I still here about ground loops, IG circuits and other things that went out about the time we threw away our bell bottoms and leisure suits.

Well another thing that hasn't been mentioned yet: the caps in the power supply of some computers can give you a nice tingle when there is no ground. Not dangerous but a pain in the rear IMO.

I apologize if folks are tired of hearing me say this, but the 'code' is neither an instruction nor a design manual. Designing 'to code' is a mythical creature, right up there with dragons and unicorns.

While that third wire was added to help ensure that the fuse blew as quickly as possible if something went wrong, it has since been used for a number of 'secret' other uses as well. That's why the code bans 'objectionable' current over the ground wire (EGC); the implication is that these other uses are allowed.

Having a GFCI will address the safety concerns of a circuit without a ground wire - but the GFCI will do nothing else. It will NOT address the other uses that the ground wire is used for.

Having said that, electronics design (the main 'secondary' users of the EGC) has progressed. The use of the EGC for surge suppression, 'phantom' loads, etc., is nowhere as common as it once was.

Plus, our understanding of grounding has improved ... to the point that a lot of the old advice regarding isolated grounds, etc., is now discredited.

My advice? Have a third wire if you can. Do not rely on the GFCI for anything except safety concerns.

I would add that I am only talking about computers, which are a lot more robust than people think they are. If you get into recording studios and radio transmission shacks, a lot of these things do make sense. I really think the urban legends about computer room requirements got started when sound engineers tried to help out their computer buddies. I watched this whole thing evolve over the 30 years I was in the biz (66-96).

Thank you all for your replies. I have a better understanding now about the grounding of personal computers and the purpose of grounding besides safety.