Accepting an offline transaction is at the discretion of the merchant, a payment terminal is going to be able to certify that a payment card is genuine, however as the issuer of the credit card may have the card reported stolen in its database, the merchant takes the risk of fraud in card-theft cases. So if as a merchant you have a well-known customer in front of you, you can still do the sale. Every acquirer can configure this to be more or less lenient for each issuer, and the tendency has been to be less and less lenient.

That makes sense, because I have paid in remote areas (no internet) before, thanks.