OK... The secret is NOW out!!!
This small islet is called Mopion
It's not easy to get to, but is it worth it!
An adventure of a lifetime, it's the getting there that is most of the story. Mopion is a classic tropical sandbar, which is held in place by a reef on it's north side. The shape is ever changing, although the area of this islet stays roughly the same throughout the year, high seas notwithstanding. The thatch umbrella, built to give a castaway a bit of shade, is maintained by the resort of Petit St. Vincent. The 22 bungalow resort is on an island of the same name, a 10 minute ride away by motorboat. The PSV resort would probably like to think of Mopion as their private property, but it isn't. They offer a day trip/picnic to Mopion, for guests to get a stranded-on-a-tropical-isle experience. Of course, all is not what it may appear to be, as there are others who come and go. Most of the time you will have this spot to yourself, but occasionally there are some passing yachties that anchor for the day just outside the shallows.
To get there on your own: It's easiest if you start in Carriacou, a small island of 7000 souls just to the north of the 'mainland' of Grenada. Carriacou is the southernmost island of the Grenadine chain, a necklace of volcanic islands stretching northward, the majority of which belong to the country of St. Vincent. And, in fact Mopion is in the territorial waters of St. Vincent, but there aren't any passport controls out here, and sailors regularly ply the waters between the two countries with impunity.
Once in Carriacou, take a taxi to the fishing village of Windward. There are plenty of men with seaworthy boats there that will be willing to take you over for a quick look, or you can do the castaway thing, and have them return for you in an hour or more. They will likely take you over in a boat the owner built by hand. Windward is the shipbuilding capital of the Caribbean, and you'll probably see numerous small boats being built on the beach.
Take some snorkel gear, water and mostly importantly, sunscreen. Enjoy!