He knows he is lying. No misremembering here. He’s looking at Letterman until he gets to the line “including the one I was in” at which point he looks down. What they call a tell in gambling. Going for the ego stroke and thought no one would ever notice.
It was an honest mistake. It could happen to anyone.
He just forgot that he wasn’t in a helicopter that got shot down in Iraq. Sometimes I forget that I’m not one of the Avengers.