I went through this just last week. If you book and pay using credit card via the Thai website (in Australia any way) then the system uses "verified by visa" which is an external automated verification process utilising the input of your OSID number on your card, which in turn negates the need to show the card at checkin.

Alternately if you ring the Thai office and pay via credit card by reading them the number over the phone you will have to show your credit card at checkin for card verification.

As an aside I also purchased tickets in Thailand last week on the website and it used verified by visa there as well.