So the fact that the generator is grounded to the frame doesn't count? It has to be a neutral bonded ground?
You have posted many popular urban myths for protectors. First, that ground is safety ground ; not earth ground. Irelevant for potentially destructive surges. A light is only reporting on what it believes is a missing safety ground connection. More on that later.
Second, a protector also does not do any filtering. Some also mistakenly believe it does voltage regulation or spike smoothing. It does not. It has a let-through voltage number on its box. That means a 120 volt protector does nothing useful until voltage exceeds 330 volts.
Third, how does that light report a defective ground? It is monitoring voltage between a green and white wire. If voltage is too high, then a 'missing ground' conclusion results. However if the generator creates tiny spikes, those spike can exceed enough voltage to trigger the 'missing ground' circuit. Those spike voltages cannot be measured by a digital meter.
Fourth, nothing inside a strip protector filters or elminates spikes that are made completely irrelevant by circuits already inside all electronics.
Your electronics connect directly to the generator by wire - if connected directly or via a power strip. What is the power strip doing?
Some generators create tiny spikes so large as to quickly degrade protectors. Honda generators generally should not. Anyone recommending protectors should know these above concepts.