Is History Correct?

I've always believed one essential fact about history . . . it's written by the winners. I just finished reading the "Sam Houston" story in "Profiles in Courage" and decided to find out what Sam Houston's role in defending the Alamo was all about. At a very in depth website on the Alamo I found this introduction . . . .

Five minutes after a car accident you can't get the victims to agree about what happened. Yet we blithely base military history on written accounts made years after the event, often by people whose sole reason for writing is to evade responsibility. Journalist interviews differ chiefly in that they draw out people who would not, by themselves, have written anything.
With the Alamo it is even worse. Many accounts that are relied on to flesh out accounts of the battle are third-hand narratives (an interview of someone who tells a story he heard from someone else) recorded decades after the battle. Joe was only interviewed briefly, and Mrs. Dickinson was not interviewed by a journalist until 1871. The last messenger out of the Alamo, James Allen, who was there for the bulk of the siege, became a Texas Ranger and lived until 1901 -- and was never interviewed at all. On the Mexican side, the accounts that do seem reliable appear to come from spectators. It may be that the intensity of the fighting was such that no Mexican in the front lines was able to write his memoirs, to put it delicately.

Anyway, Sam Houston was an amazing man. He was steadfastly against secession from the Union by Texas and captured General Santa Anna shortly after the Siege of the Alamo. Governor of Tennesee, Senator and Governor of Texas.