What's the issue with the zero emissions rhetoric?

There are still emissions during production and decommissioning. And cars are sources of noise and light, and emissions due to component wear (tires and brakes, probably others as well). A specific car may be not as bad as others for the environment, but there is always some impact.

I guess the complaint is that electricity production is not zero emissions in most of the world, so it could be considered misleading.

I don't think it makes sense, ICE vehicle emission ratings have never included the drilling, refining, and transportation of fuel, and the alternative is for every vehicle to just advertise "unknown emissions" because it's impossible for the manufacturer to know anything beyond what the vehicle itself produces.

It's not legal to operate on public roads without a human behind the wheel and humans are known to emit CO2.