Not necessarily. For example, during the impeachment of Trump, there were peoepl like Rice who when testifying to Congress in private, said she knew darn well there was no Russia Collusion. But in public: they are said the opposite. When under oath especially if the opposing side has the goods to dispute your lies, people will often times tell the truth.
Good point. Like Brennan and Shiff who told the media they had absolute proof of Trump’s Russia collusion but under oath didn’t say that.