Normally when u r flying with the airline
u just need to show them your booking confirmation ...
You might want to check that statement with relation to Eva Air.
At my wife's company their admin booked flight for their employee on SFO-TPE-SIN on EVA using company's president's card. The flight is leaving at 2AM from SFO. At the airport they requested to see the card, which the guy obviously did not have. They refused to let him onboard and requested to buy new ticket.
Long story, but they had to wake up president so he can explain over the phone that the card is his and he authorizes the person to fly.
After that the admin was fired and there is now company policy no never buy any flight on any airline requiring credit card showing at the airport.