Does the author believe the story of the sweetheart of the Song Tra Bong? Cite evidence supporting your answer.

The author does not believe the story.

Vietnam was full of strange stories, some improbable, some well beyond that, but the stories that will last forever are those that swirl back and forth across the border between trivia and bedlam, the mad and the mundane. This one keeps returning to me. I heard it from Rat Kiley, who swore up and down to its truth, although in the end, I'll admit, that doesn't amount to much of a warranty. Among the men in Alpha Company, Rat had a reputation for exaggeration and overstatement, a compulsion to rev up the facts, and for most of us it was normal procedure to discount sixty or seventy percent of anything he had to say.