I guess the non-secret parts of the card number can totally be cross referenced with others merchants you've shown the card, but an online purchase very often also has a name and address so your identity is already out the window.
Also fraud detection systems will often track the type of purchases associated with a particular card number, to detect anomalies. So I suppose your privacy is somewhat protected from that, but the e-commerce sites probably already know who you are.
I agree that as a potential customer my main interest is about credit card theft/abuse.
(This does make me wonder if they are mis-marketting focusing on privacy, instead of controlling damange of credit card theft, and sketchy merchants who charge you reoccurring charges you didn't realize/have trouble canceling, etc. That's my interest).