Fridge Horror: Berger didn't die in combat. The chances that he would get all the way to Vietnam without anybody noticing this guy doesn't belong there are about nil. But they don't know how he ended up there, nor would they be likely to ask, so it's likely they assumed the worst, and shot him. Then, when they found out the error they'd made, they were probably so embarrassed, they would've put pressure on his family and friends not to tell a living soul about this unfortunate incident.
Wild Mass Guessing: Related to the above. In the film, Berger's name is on the tombstone. Which means the mistake was figured out. And now Claude is wanted for being a military deserter. Or legally dead.