Credit card payments have an "offline" mode for the same reason - before ubiquitous broadband, a shop may have to dial-up to the bank to verify a card, which is slow. Debit cards that run on the credit networks can have that enabled or disabled depending on trust.

Remember originally credit card payments worked by putting the card under a slip of carbon-copy paper and rubbing off the raised digits. All the digital stuff ontop of that was just for efficiency.