Credit card fraud is rampant so clearly retail establishments need to initiate processes that help to curb the process. However, do not let processes create a situation where you are generating customer resentment rather than customer advocacy. Everything is in context. If the credit card signature does not match the card exactly do not ask for a ID. A proper response would have been, "your signature does not match the card, do you have an ID?" Provide a reason for the inconvenience or better yet consider the context of the transaction and let it go!
The business process in this case questioned a legitimate transaction and has now lost me permanently as a customer. So if the aim was to prevent fraud, it failed brilliantly.