The book is A Brave Vessel by Hobson Woodward. This from an article in ROROTOKO written by the author:

In addition to rediscovering the work that preceded mine, I made some discoveries of my own. One of the most important was the realization that two Powhatans of Virginia were almost surely aboard the Sea Venture. The greatest chronicler of Jamestown, Capt. John Smith, alleged that they were present on the vessel when it wrecked, but scholars have doubted his account because he waited fifteen years to publish it. By drawing attention to a hitherto overlooked source that dates to just after the castaways returned home I was able to show that Smith was almost surely telling the truth.

The two Powhatans were very likely aboard the doomed vessel, and, as Smith alleges, one probably did die on Bermuda. Smith claims that one of the men murdered the other on the island. While I suggest that the “murder” was more likely a misunderstood accidental death, I nevertheless corroborate the basic facts of Smith’s long-questioned account.

One of the fascinating results of my showing that the Powhatan voyagers were almost surely on board the ship is that it is now clear that a tale of alleged murder by an island-bound Native American reached London just as Shakespeare was composing his play. He is thereby provided with a model for Caliban, the murderous wild man of The Tempest.

Literary sleuths have long seen Caliban as a portrait of a New-World man as seen through a filter of Jacobean culture. With the publication of A Brave Vessel, scholars no longer have to depend upon vague generalities when drawing that comparison. They now know that a story of a supposedly murderous New World man marooned on an enchanted isle reached Shakespeare just as he was creating his Tempest. Thus the Powhatans’ presence on the Sea Venture has as much importance to literary history as it has to the history of America.

The rest.

I’ve always been struck by how prescient Caliban’s most famous speech from The Tempest is. Right down to the last three lines, which are as good a description of the American reservation system as I’ve yet to find.

This island’s mine, by Sycorax my mother,
Which thou takest from me. When thou camest first,
Thou strokedst me and madest much of me, wouldst give me
Water with berries in’t, and teach me how
To name the bigger light, and how the less,
That burn by day and night: and then I loved thee
And show’d thee all the qualities o’ the isle,
The fresh springs, brine-pits, barren place and fertile:
Cursed be I that did so! All the charms
Of Sycorax, toads, beetles, bats, light on you!
For I am all the subjects that you have,
Which first was mine own king: and here you sty me
In this hard rock, whiles you do keep from me
The rest o’ the island.