I've had these checks a few times recently in Asia. Luckily, I had the right card on me. I can't say that I usually would (US airfare would have gone on a card I don't carry, but that has a forex fee).

So what would happen if I didn't have the card? I'm done, or do they have an alternate verification method?

Next, what happens if your company's travel department books the ticket on their card or account?

Been curious about this.