Yes, you need both vent pipes. The one for the black water tank you understand.
These trailers were originaly set up to hold only the black water, the grey water was just dumped on the ground or, in some tralers, sent to the black water tank.
If the black water tank is holding only black water it is shut off from the grey water. Thus, the grey water drains need a place to vent or you stink up the trailer.
I have a later model trailer with both grey water and black water tanks. The vents join together and go to a single roof vent.