Not a myth. This is true, or at least very likely. There is strong evidence that Shakespeare did use elements of the story of the wreck of the ship Sea Venture in his play, The Tempest. The ship was on its way to Jamestown, Virginia, in 1609 when a huge storm, probably a hurricane, blew it onto the uninhabited island of Bermuda. There the survivors salvaged everything they could from the ship and built a new one from the salvaged parts and the local cedar. Months later, they made it to Jamestown where their arrival saved the colony from abandonment. According to Colonial Williamsburg research files, “An account written by one of the voyage’s members, William Strachey, entitled “A True Reportory of the Wreck and Redemption of Sir Thomas Gates, Knight” (Gates was the future governor of the colony and a leader of the survivors) was sent to an anonymous noble lady at court. It was not officially published until 1625, after The Tempest was first performed, but many scholars agree that Shakespeare was at least familiar with the story and incorporated parts of it into his tale of a shipwreck on a mysterious island.”
For more details, see Louis B. Wright’s A Voyage to Virginia in 1609 (1964) which republishes Strachey’s “”A True Reportory” and another primary account, Silvester Jourdain’s “Discovery of Bermuda.” Either or both of these could have been Shakespeare’s source. Or Hobson Woodward’s A Brave Vessel: the True Tale of the Castaways who Rescued Jamestown and Inspired Shakespeare’s The Tempest (2009).