I looked at your initial post again and see that they mentioned the generator's frequency wave was not clean. I'm wondering if instead of a sine wave your generator is producing spikes somewhere in the wave. The frequency can be spot on at 60 hz and the wave pattern itself can still contain spikes or odd shapes.
Not sure how it works exactly, but if your generator uses brushes and copper commutator, I'd imagine that a little buildup in the wrong place could create spikes in the wave pattern. If the generator people are measuring the voltage and freq, they wouldn't necessary notice spikes in the wave pattern or oddly shaped waves.
Not sure if the inverter/charger is sensitive enough to the wave pattern to detect this, but that does sound like it could the kind of thing they're talking about.
