The cover for the airbox on this Honda generator hinges open to the left, but the frame rail is directly in front. The airbox is also bolted to the engine from inside (behind the filter).
I've throughly looked over this and there is no way to open that airbox unless you unbolt the engine from the frame, or perhaps modify the lid hinges with a saw so it doesn't have to swing as far to come off.
The orange cart its sitting on is just for moving it around. The generator itself is built/branded Honda, not just the engine.
Yeah i would be surprised to see a Honda branded engine in some third-party generator since they sell generators themselves.