Technical article from Blue Sea Systems
The green wire referred to in this "controversy" is the safety ground wire that connects the DC negative ground block to the AC safety ground bus. The purpose of this wire is to provide a lowest-resistance path to ground for any stray AC current that finds its way onto the DC ground system. There have been cases of AC current entering the water through the engine shaft and killing swimmers near the boat. This wire is "controversial" because it can also provide a path for galvanic current if the boat is not adequately protected with galvanic isolators. However, most marine industry organizations and professionals now consider it standard practice to install this wire.
Original article from Blue Sea Systems