My sister flew MAD-LHR two years ago, and had bought the ticket herself with her own debit card. Two weeks before flying, she realised she'd have excess luggage so I logged into her booking and prepaid for an extra checked suitcase with my own credit card.

When she tried to check-in at MAD, they wouldn't issue any boarding pass until she could provide the credit card used to prepay for the extra suitcase. She tried to phone me to confirm the number, but alas I was halfway across the Atlantic on a B747.

She was denied boarding, and ended up going across to T1 and booking a cash ticket with Air Europa to LGW for £150 (extremely reasonable for a walk-up ticket!) BA were very nice about it afterwards though and gave plentiful compensation once we threatened to take them to court.

I understand the need for verification due to fraud, but sometimes it really goes too far.