That is correct, kind of. The reason a safety ground is required, and can’t be smaller than the power conductors is the need to carry 100% of a shorting current. That is, if your equipment has a 10A fuse or breaker, the safety ground must be able to carry that current amount safely, but if all is well that current should not flow. However, the construction of a metal chassis which is grounded is rather like a Faraday cage so we expect that RF noise should be greatly reduced vs. a plastic enclosure.
The use of cheater plugs to lift the safety ground becomes a problem when a short happens. The 10A of current, or higher now has to travel 24gauge ground wires in the signal cables, potentially causing a fire or minor explosion or both. If a wire melts fast enough it basically evaporates with a bang.
The problem is how equipment makers connect a signal ground to it, and the center tap of a transformer secondary. In an ideal case there would be no metal to metal path between a signal ground and the chassis, or when used, would not carry from component to component.
Even digital devices can have ground loops as a result of non-isolated coaxial or USB inputs.
The best cases are the use of XLR connectors which allow the lifting of ground on one end or the other, eliminating the loop itself.
@cleeds I think you are mixing up 1980’s appliance manufacturing with audio gear.
I can’t think of any piece of audio gear manufactured in the last 50 years which would do this, balanced or unbalanced. It would violate several codes and set you up for some really nasty noise and safety problems if this was true.
I think @cleeds brings up a good point by accident.
The reason ground loops in audio gear happens is probably due to historical oversight.
Stereo appliances went from being all in one units without grounds to separates with a separate chassis ground and, at least for unbalanced signals (using RCA) , never quite reconciled the difference between a signal ground and safety ground.
This article may help. Apparently ground pins started appearing in 1967. For some reason people still think of Neutral and Ground as equivalent but don't ask, if they are the same thing why are they on separate pins and conductors?
I'll add something that is somewhat obvious but some may not understand it: Neutral and ground, being tied together at the panel, will both "work" to run a piece of equipment. So if something is wired wrong, there may be no indication until something shorts. Also you might get a bit of a tingle touching the frame which would indicate a problem.
And in Audio Equipment, you can get a noisy ground loop.