I think I understand why Brian Williams made up his story about being in a downed helicopter in Iraq--he wanted to be the hero of his own story. Narratives, especially one of your own devising and where you're the central character, seduce.
I have no doubt as well that he really did come to believe his falsehood. Think of Don Quixote crafting stories about his heroic adventures. He too lost track of reality.
But the fact remains that Williams wasn't on the copter that day in 2003. He was an observer--not the center of the action, but on the periphery.
Interestingly enough, so too was Chris Kyle, the hero soldier whose tale is told in American Sniper. He spent his time on rooftops, looking down on the bloody battle below. He escaped the horrors encountered by the grunts on the ground. It's true he was a world-class sharpshooter, but wars are not won by sharpshooters picking off targets one by one. They are won by soldiers carrying out mass killings.
Nonetheless, Kyle is now regarded by a large segment of the American public as an icon of all that is good, noble, and self-serving about this country. It's the same lie of the mind that enabled Williams to believe his own falsehood. We have cast ourselves as the heroes of our own story.
The narrative in American Sniper is just as seductive, just as easy to become lost in.