Strong stats:

In 851 flights over the last 8 years, in 5 continents (none in Oceania, though), I was asked to show my CC twice (0.23%), both times by TK agents in ATH. On one of those I didn't have the CC with me, for reasons that are too long to explain here but which convinced the checkin agent and they let me fly to the US.

As for this present thread, if I were the OP I would try hard to worry less and to not get upset because an airline employee and a bunch of FTers don't share the worries: you significantly increase the risk of a heart attack! Believe me, I know exactly what I'm talking about...