One would naturally assume they come from Tahiti...

Tahiti is actually the market for Black pearls from the islands and atolls of French Polynesia, the Cook Islands and Micronesia. There are other black pearls grown in Japan Thailand and some in the Philippines, but ONLY pearls grown in French Polynesia can be called Tahitians.

It is mostly the islands and atolls in the Tuamotu Archipelago and Gambier Islands that have the production of Tahitian pearls. You might have heard of Robert Wan? He owns the island of Marutea sud and he grows the most of the high quality Tahitians. Because of his marketing efforts, Tahitians have become some of the most desirable pearls. 

Under the heading of the more you know,Tahitians are black saltwater pearls with overtones of greens, blues, roses. There is no such thing as a natural black freshwater pearl. All black freshwater pearls have been irradiated to create their black color. Not good...