Mr. Bobcat,
HF can do strange things. One thing you need to be aware of...Any AC/DC Tig unit that is a transformer based machine has continuous HF.
In laymens terms, the separate grounding is to drain off the HF Voltage that builds up. HF likes to jump across circuits in units and find its own path to ground. It can mess with internal circuitry as well. The grounding screw on the back of many units, gives the HF buildup a place to drain.
IF the company recommends it, then, I would use it. HF emissions can be greater by having poorly gapped points or circuits that are poorly designed.It can even kill your own machine. It doesn't take much, but a good wire should stay attached if a ground is recommended. The ground is more of an "earth" and should not be run back to the panel box...unless you want "real" problems.
Typically, inverters that use HF for starting, have HF engaged for 2-5 seconds at most. They are likely to cause less severe interference.