As well as during the booking process on their website, they also send the following email too:

"Dear Mr. xxx,
Greetings!!!
We have received your online reservation made on xxx for your travel on dd/mm from xxx to xxx.
This is therefore to kindly remind you to bring the credit card used to the airport while you are coming for check-in as it is required for verification or you can contact the nearest Ethiopian airlines ticket office before the travel date and verify the card. Failure to present the card at check-in or at the ticket office will result in a new payment for the journey being required.

<snipped out local office details>

For any further inquiries you can reach us on +251115178759 or reply to this email.
We sincerely apologize for the in convenience this might cause you and Ethiopian wishes you a very pleasant journey.
Kind and best regards,"

It seems like a perfectly reasonable policy to me. However, if for whatever reason, the passenger is unable to produce the card it would be much more fair on the passenger for the airline to refund the original card and request payment on another which seems to be suggested in the above email.