U.S. Navy bought them in batches from the same places as the War Depeartment. They arrived with the factory green finish.
Now, USN pratice was to paint things the same color as they were stored. So, if you reported to Mount 42, second 40mm mount, your helmet was in a rack alongside that mount, and you donned it when GQ was called away. Since the helmets were in a rack, they were painted the same as the surrounding area. Now, unlike other Service, the helmets were issued to the station on the ship, not the person manning that station.
Now, that was practice in the "steel" navy, the folk in PT's and the like came from that tradition. So, if the Chief had cadged of comshawed green paint for the boat, then there'd be green paint for the helmets. Those helmets could have been painted any handy color of "grey" at what ever supply depot they were recieved from, too.