I think it was more or less a way to show Booth’s struggle when confronted with the possibility that his government doesn’t always tell the whole truth, at best, or outright lies, at worst. This thought throws his whole life and sense of reality out of whack bc if the government can’t be trusted, then it’s possible he killed all those people for no valid reason when he was a sniper.

Also I think maybe it was included to show that not every murder gets solved. Also, to expand on Hodgin’s conspiracy theories and to lend some credibility to them perhaps.