No, there's not much truth to it. That is, there's a little bit, the basic outlines of the war, of course, and the fact that southerners suffered a lot in the Civil War and in the years afterwards. White southerners were seeking a way to show that their suffering was unjust, but that their actions were heroic and just; that they could be proud of their relatives who had fought in the war; and that there was truth to the violent racism they practiced. Birth of a Nation was very pleasing in accomplishing those goals, even though they were not historically valid or truthful. The movie is largely a mythmaking enterprise, codifying the story the South wanted to tell about the greatness of slavery, the terribleness of free blacks, the stupidity and childishness of black people, the wild animal lust of black men for white women, the lack of honor of northerners, the great suffering of southerners, how awful misegenation is, and the greatness of the KKK in restoring order and saving or avenging white female virtue. Most of the elements of this narrative were included in the novel Gone with the Wind as well, and permeate political and social discourse about the war today. These elements became more muted in the film Gone with the Wind, due to the code of propriety then in existence in Hollywood. You may want to read D.W. Griffith's the Birth of a Nation: A History of the Most Controversial Motion Picture of All Time by Melvin Stokes. It goes into a lot of detail about the film and the effects it had, as well as how it depicts American history.

Completely agree with bettinafairchild. In terms of asking how it was justified, I wanted to add that Woodrow Wilson gave it legitimacy as well. It was the first movie shown in the White House and the president promoted the film's importance after viewing.