A psychopath passes a lie detector test because he truly believes everything he says is the truth.
I have a bipolar, Xanax addicted in law like that. She got pissed at me for calling her stupid (she is) and began telling my wife that I was stalking her. After she told the story several times, she came to believe it actually happened. I guarantee she could pass a lie detector test claiming I stalked her.
I know two people like that. They say something and keep telling themselves the same. After a sort time they really believe it.