The rules are that you can use the word 'genuine' with cultured pearls, but never natural -- unless it directly modifies the color term. So, 'natural pink pearls' legally means something entirely different from 'pink natural pearls.' Of course, hardly anybody knows this and the term 'natural' is misused all the time. The only alternative I know of is to call natural pearls 'wild,' as opposed to 'farmed' for cultured pearls. Most people know the difference between, e.g., wild and farmed salmon, so that might help!
The Pearl of Great Price was not something farmed by Mikimoto