It does! As you can see in the diagram, that green wire connects to many different electrical components as a ground.
The small symbol with three parallel lines indicates ground (bottom green arrow). If you took the black wire that you were hooking up to the black wire from the harness to the green from the generator,
and have left the other black connected to the green through the plastic connector, both are grounded which is why you are not blowing a fuse. However, the reg/rec has no power now since you have grounded out both black wires.