My take on this issue:

If you are using double insulated tools or appliances that by design do not have a ground pin on the plug, then you're OK not grounding the generator.

If you are using tools or appliances that do have a ground pin on the plug, then you really should ground the generator. It seems that simply grounding the tool or appliance to the generator frame does nothing from a safety standpoint. After all, the safety function of the ground is to draw off current of an unintended /unexpected short occurs in the appliance.

When a teenager I was sitting on a carpeted floor pinning large pieces of fabric (making a Frostline tent, if you remember those). I was using a 36 inch steel cased fluorescent light laying on the floor as an extra source of light. At one point I slid the light to the side, it touched the heating vent grid, produced a large spark, and popped off the circuit breaker.

Clearly there was a short in the light that charged the metal case, and I assume (I can'tremember for sure) that the light was not grounded. Had that metal case been grounded, just plugging the light in would have popped off the circuit breaker, safely handling the shorted condition.

If I had happened to have touched a heating vent cover with a foot while touching the light with a hand, that current would have gone through me. Scary!