I know to many this seems like a ridiculous thing to lodge a formal complaint about, but it's not.
Visa, Master Card, and American Express all have clear rules that their card members aren't supposed to be harassed for ID if their credit card is signed. The merchant is only allowed to check the signature on the card and verify that it matches the signature on the receipt.
If someone asks to see a driver's license when you're using your credit card, you should refuse, and you should report them to the 1-800 number on the back of your credit card.
Credit card companies specifically state that the only time they are to ask for ID is if you hand them an unsigned card. If you give them an unsigned card, the merchant should ask to see a photo ID, and the merchant should require you to sign the card in front of them. If you do not have a photo ID, or if you refuse to sign the card in front of them, the merchant is usually supposed to keep the card and treat it as stolen.
As long as the processing system authorizes the card, the credit card company guarantees the purchase, so the merchant has nothing to worry about even if they do think the card is stolen. If the card is approved, it's really none of their business.