One additional data point:
Redeemed 50k BA miles on a CX flight some months ago. CX agent at SFO wanted to see the card used to make the "purchase." I told her it was an award ticket and only taxes paid. Since it was an old card (churning!), no longer had it. I offered to find an old statement on line, but she was pretty resistant. Only after consult with her manager and me verifying other pieces of information such as ticketing date, did she eventually overlook the credit card requirement.

Only twice in my history of flying...15 years or so, has credit card used for payment ever been requested.