I think the only person entitled to see the card is the merchant that sold the ticket, at the time of the sale. And even then, per agreements with merchants and the credit protection act, no ID is required, just signature match. If the AIRLINE sold the ticket on-line, then requesting the card at checkin is acceptable since they are the merchant and should have the card present to conduct a sale anyway (just like a Hotel should always get an imprint of your card and signature when you check in).
I use American Express Private Payments when I shop online, so the number used on the ticket wouldn't match my card # anyway, oh well...I just can't win... :-)