If you see the message, it will happen. I've flown KE over the years on many kinds of tickets (travel agent, awards, etc.). The one time I actually purchased direct from their own Korean Air website, that message popped up...and sure enough, she asked for the card at check in.
BUT be careful. I also used an American Visa card on their Korean website (this was bought in maybe October 2015 for a flight in December 2015).
To make sure you are safe, you should be able to mail a copy of the credit card front and back to Korean Air and they should be able to clear the security flag that way.