nugget of truth
A singular element of truth or wisdom within or among a greater story, narrative, speech, or claim, especially when most or all other elements are fictitious or of questionable veracity. I think the governor's speech is a bunch of hogwash by and large, but there is a nugget of truth in what he said about the need for lower taxes. Conspiracy theories survive because they are usually laced with little nuggets of truth that give them the air of credibility.