I can't believe the point isn't getting through. I'll take my shot at it.

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A is on the no-fly list. He is trying to fly.

B is not. The airline Computer expects B.

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A brings the following things with him to the airport: ID A, Ticket A, Ticket B

Security: Ticket A vs ID A

Boarding (America): Ticket B vs Computer (B)

Boarding (Canada): Ticket B vs Computer (B)... vs ID A