I remember a colleague having similar issues a few years ago at BOM.
He is based in the UK but had bought tickets for his parents using his UK credit card.
(he was not travelling)

They asked for the credit card when his parents went to check in and they were told that they couldn't travel without proof of the card .

My colleague then had to fax an authorisation letter with a copy of the card to DXB/BOM???? And it took several phone calls to EK offices before they were allowed to fly.