A classic example of how even primary sources can be inaccurate is seen in how the original "eyewitness" of the 1619 arrival of the first Africans to present-day United States deliberately lied about the ship that brought them.
Virginia colonist John Rolfe (famous mainly as Pocahontas's husband) described the ship, the White Lion, upon its arrival as a "Dutch man-of-war." However, even primary sources—so sacred in historical research—are often discredited upon subsequent research. Rolfe was British and didn't want to admit that the pirate ship delivering the Africans was British-owned, and so he wrote that the ship was Dutch. His assertion was considered true for centuries until corrected relatively recently.
Regrettably, by trusting Rolfe's account, I fell for his ruse when I wrote Esteban: The African Slave Who Explored America and reported that the White Lion was a Dutch ship on page 202. An aristocrat in England (Robert Rich, the Earl of Warwick) was the ship's actual owner.
I apologize for spreading the error wider and stand corrected.