All sorts of 'verify by Visa' rely on 3DS (Three Domain Security) and were designed specifically for online transactions. They do not really exist for offline transactions as there is an assumption a seller will either verify the signature (not really used any longer) or cardholder will authenticate via PIN. Sale via the call centers is harder to authenticate and many vendors established additional verification methods (like sophisticated fraud checks - these are performed by specialists like e.g. Accertify and are relatively expensive). Showing a card at product pick-up is a reliable and cheap fraud check method
US issued cards do not have this European 3DS and Chip+PIN nonsense. They are designed to protect the merchant, not the consumer anyways. Why do I have to prove it to the merchant every time I want to make a payment?
I can use my US based card globally right away without being bothered to enter a secondary code. If the merchant does not accept my US card for lack of 3DS, they will simply lose my business. And if my card were misused, the bank would refund it immediately with no questions asked.
So European Airlines may be treating tickets paid with US credit cards with more scrutiny.