Thanks,
littlegreenman.
I have no wish to turn this into a contract law forum

but it seems to me that Section 6 of the Unconscionable Contracts Ordinance (modelled on the UK's Unfair Contract Terms Act 1977) is most relevant here:
(1) In determining whether a contract or part of a contract was unconscionable in the circumstances relating to the contract at the time it was made, the court may have regard to (among other things)-
...
(b) whether, as a result of conduct engaged in by the other party, the consumer was required to comply with conditions that were not reasonably necessary for the protection of the legitimate interests of the other party
What we have here is a contract whereby my friend agrees to pay the fare and EK agrees to fly her to the UK and back. EK is effectively saying, if you have chosen to pay with a credit card, you must then show me the credit card, otherwise you breach your agreement to pay and I don't have to fly you to the UK and back anymore. No, once you have chosen to pay with a credit card, you cannot not show the credit card. And no, you cannot pay by any other method, not even cash. If you lose your credit card, forget to bring it or have it swallowed by a machine the day before you travel, tough luck.
I do not think any reasonable judge is likely to rule in favour of EK.
Anyhow, let's say that the legal position is at least arguable. The point is, even if EK prevails when it comes to the strict legality of the matter, with this sort of incidents happening at least from time to time, why can they not, for the sake of good customer relations, devise a set of sensible solutions rather than be seen to profit from fairly innocent mistakes by their customers? How many of us can say we have never lost our credit card or left it at home by mistake?
That is what we do not understand.