The problem is that we do not always know whether stories are true or not. As far as I can tell, the events discussed by Dr. Schama are true - so why raise the question? However, the matter becomes acute when it comes to the Scriptures, where many of the narrated events do not seem to be true.
An ingenious solution to this problem has been proposed by the brilliant German scholar Jan Assmann, who supports the idea of "mnemohistory." In a nutshell, mnemohistory addresses what people remember to have happened, disregarding any strict canons of historicity. But does this approach solve the problem? In the relatively recent case of American history, many people "remember" things that never happened. At all events, here is Assmann's recent summary of his findings. http://www.amazon.com/