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.
I can't tell from the photo. Is it possible the airbox is installed upside down? As in, if you were unbolt the frame once, could you unbolt the airbox itself, flip it 180 degrees and would it mate to the surface the same what allowing the airbox be able to open with the frame in place?
No; it bolts directly to the carburetor. If it was flipped upside down (vs the current orientation) it would be running into the fuel tank/upper frame rail. Then it would hinge open in the other direction, but still hit the frame and be stuck shut.