Perhaps one of the more embarrassing, if not shameful, scenes of the New Testament was Peter’s denial of Jesus. Even after everything he’d witnessed, Peter openly denied—even vowed—that he never knew Jesus, for fear of his life.
Openly admitting you are a coward—willing to go as far as to swear falsely—would seriously undermine your message if it was false. Why should people trust you now, when you lied to them? Therefore, why would this be recorded if it wasn’t true?