That does seem to be the story we hear the most, but I have a different story.

It is common misconception that Mikimoto invented this process. But Mikimoto acquired the culturing of pearls from Dr. T Nishikawa's research through marriage to Nishikawa's daughter. 

Dr. T. Nishikawa of the Tokyo Imperial University first discovered the technology to produce spherical "akoya" pearls. In a letter he wrote in 1907, he stated: "It is a great pleasure for me to tell you that I am studying pearl formation and pearl-oyster culture work this summer (1907). Fortunately, I have found the cause of Japanese pearl formation, i.e. the reason why and how the pearl is produced in the tissue of the oyster. I made a practical application of this theory with great prospects for producing the natural and true pearls at will." (Kunz, George Frederick. The Book of the Pearl. New York: 1908. pp 292-3).

It is Nishikawa's work that changed the science of pearl culturing from shell nucleation to tissue nucleation. After receiving his patent in 1916, round Japanese akoya entered the pearl market for the first time. However, Mikimoto became famous for inventing round "Akoya" pearls from the P. martensii oyster.