That may be easier said than done.

Plus, I bet the ticket (or check in, or gate) agent did not really have much discretion. AC has a rather aggressive fraud dept, and surely these cases occur because flagged by the fraud dept. Which likely also specified how much latitude the agent had in verifying the CC.

But airlines cannot do much beside denying boarding when suspecting credit card fraud.

I have been on the opposite end of this a couple of times, when some random tickets appeared on my CC. After I complained they reimbursed, but since the tickets had already been used, the airlines swallowed the loss.

This said, in some instances in the past, I was under the impression that AC's fraud dept occasionally had gone beyond what contract law allows.