Looks to me there are two different discussions going on. The need for a ground and the current flow over a wires surface.
It's true current flows over the surface, so the bigger the surface the more current it will handle.
The need for a separate ground on equipment, other than the 3rd prong, has been debated forever. All things being equal the 3rd prong on a plug should be the same potential as any other ground in a building. But should the grounds not be consistent or a bad joint in the ground that's where the trouble lies. That's why I prefer a ground from the power panel all the way to my equipment. Than I know I'm the same potential as the rest of the buildings grounds. If I get a dedicated source of power for my equipment and my equipment only, that also satisfies the grounding requirements. I'm finding more and more that is hard to get.
What causes the harm is mis-grounding. You want your equipment to be the same potential as any other ground, not better, not worse. That's the key.
EDIT: Want to ad. The proper way to check ground potential is to meg it to earth. Nobody does that anymore. A pretty good source is to drive a ground rod and the soil conditions dictate how deep or how many, than check your ground to the rods you've just driven, shouldn't be any more than a half ohm difference in the two, if there is you need to start looking for your grounding problem.
The statement as to how deep or how many relates to the following saying we had back in my Northwestern Bell days. Ground is ground the world around, except in the Nebraska sand hills.
