No, the CREDIT card customers are immune from any responsibilities. If the customer timely reports the card lost or stolen, customer liability is capped at $50. And many issuers will eat that first $50. Generally, the bank will get stuck, but they might try to recover from the merchant in some cases, depending on the size of the loss, merchant culpability, and the customer relationship itself.
Rules are different for debit cards, which is why I won't use one. Although, again, the bank will sometimes eat the customer's share of liability or share the loss and treat it like a credit card loss.
I never said they weren't. There are four parts of a credit card transaction with a company like VISA: (1) VISA, (2) the financial institution issuing the VISA credit card, (3) the merchant, and (4) the consumer. VISA has literally ZERO responsibilities in any fraud case. The consumer rarely gets stuck with any liability. It generally falls to the card issuer and the merchant. Despite the rules, you would be surprised how many times the card issuer gets stuck with the "bill" behind the scenes.