Another data point: The last time (only time?) I've been asked to show a credit card was a Delta award flight in 2010. My Mom had booked an award ticket for me to fly ORD-JFK-CDG-XXX, and I was meeting up with her at JFK. They asked me for the credit card, which was my mother's and not in my possession. I explained that and they then tried to call her, which was fruitless since she was en route to JFK at the time. Within minutes they'd shrugged it off, tagged my baggage and sent me to the gate.

No European carrier has ever asked me for my credit card, nor have I been asked on any flight originating in Europe.