If it's billed as a centralized account, the reservation probably also shows as being booked by a travel agent or corporate travel department, which will waive the credit card requirement.

What they're trying to avoid is the scam where a stolen card is used to book tickets. If the tickets are for flights a short time after booking, there may not be time for the fraud to be detected and the chargeback to work its way back to the airline before the flight.

Typically the person stealing the card isn't using the tickets, he's pitching discount tickets to other people. They pay the thief cash, at much less than face value. That's also why "3rd party" tickets (flyer is not purchaser) get extra scrutiny.