score:20
Until you showed the boarding pass the only evidence you had that you were telling the truth about who you were and what you were doing was a single ID card.
Against that were a bunch of fairly unlikely coincidences that implied that you might not be who you said you were.
With a second piece of corroborating information that matched what you claimed and what they knew, the odds dropped that you had, say, picked up someone else's ID card, so they let you through.