I think some airlines pick a few passengers at random to ‘fraud check’, If you book the day before you’re pretty certain to get asked. If you book a few days in advance through a third party you’re pretty certain to get asked. BA ask a lot, and it tends to be weighted towards the States and Dubai for whatever reason. They tend not to be overly strict though.
Book direct with any airline quoting your frequent flyer number, and they know who you are so chances are slim.
The headache for me personally is TAP. A fraud check involves a phone call to Lisbon and they are strict, if the card isn’t there then they expect you to buy another ticket. With a big percentage of passengers heading to Brazil that isn’t cheap.