If there is current flow, there must be a path.
The NEC grounding requirements are that in the event of a short to the chasis that path be as low an impedance as possible.
Star Grounding and the Home
This comes up a bit so I wanted to talk about it.
You may not, for safety reasons, create a separate grounding scheme for appliances fed from the same service. May. Not. Ever. That means that at the service entrance all the grounds and the neutrals must connect, preferably with zero Ohms between them and zero Ohms to the ground rod(s). I say preferably because, corrossion, splices, etc. These are rarely perfect.
However, you MAY run an insulated separate ground wire to the ground rods which feed the rest of the home. This is like a star grounding scheme in a piece of audio gear. You meet the code criteria, and you hopefully dissipate noise in the ground wiring of your home at the rod before it can reach your gear. You can achieve a very good version of this by running a sub panel to your audio room.
One interesting possibility that I’ve seen some power conditioners hint at is to use a coil with appropriate gauge wiring and low DCR to isolate the gear. This meets the code requirements that it can carry 100% of the current in the event of a short, and the coil blocks noise from the rest of the home. Pricey, cause it requires heavy coils, and because.... audiophiles.