You are always free to book independent tours, but just make sure that your operator can guarantee your return to the cruise ship well before the departure time.
For example, we booked a 1/2 day snorkle and fishing excursion in Hawaii, and I asked the operator a lot of questions. Mainly, if something happened to his boat, what was his back-up plan. He assured us that he had contacts on many boats in the area and that someone could pick us and return us to the small boat harbor.
Quite often we have booked our own tours or just ventured out on our own. The price is certainly cheaper.
However, there are some excursions that are only available through the cruise companies. For example, the folkloric performance by the Papantla Flyers in Mazatlan, Mexico is an exclusive offered only through cruise ships. You just can’t book this tour independently.
So in Tahiti, look at what your cruise line has to offer, then get on the web and compare prices and amenities to what you can book independently.
I hope you have a great cruise and let us know what your decide to book in Tahiti.