Pardon me if I don't see the issue here.
Are not neutral and ground normally strapped together at the distribution panel?
Since the genset is the power source, distribution panel and outlets all in one, wouldn't it make sense to strap them together there?
Or should they be strapped together before the run to the outlet?
Since the frame of the generator MIGHT be grounded, I would want a nice solid return path in the event that hot shorts to a metal chassis in a tool that I'm using. Better to trip the breaker than have 120V AC finding a convoluted path through my body, into the ground and back to the genset...
Correct my amateur self if I'm wrong.