My two generators, a 5500 watt Generac open frame and an 1800 watt ETQ inverter generator both have ground lugs and both say to ground them for safety sake. I seldom do this, and my take on it is hardly anyone else ever does it. But I'll bet that doing so would also solve the issue.
The Generac is for home use, and I drove an extra 8 foot ground rod into the ground next to where that generator would sit when using it to power the house in the event of an outage. But I note that one can as easily get a good ground the old fashioned way: with a battery clamp on a water faucet that has metal pipes.