Why would they? They didn't make store policy.
You don't seem to understand how credit companies work. They have no clue what you're being charged for. When a vendor posts a request for a charge (pick a credit card company), the only thing they know is the name of the requesting vendor, and the total. From there, they do this:
- Do you have enough of your credit line open to make the purchase?
- Has there been a recent rash of atypical charges, which would suggest your card is being used for fraudulent purchases?
- Are you a credit risk (lots of late payments or other reasons why they may deny a large purchase)?
- Maybe some other check boxes they have.
If everything is flagged green, the purchase goes through and the credit company pays for your items on the (obvious) reliance you will pay them back when you get your monthly bill.
Look at your bill. If you bought something at a gas station, it will likely list the station's name you were at. But that still doesn't tell the credit card company you bought gas. You could have parked in front of the convenience store area and bought a handful of frozen pizzas, a gallon of milk and a six pack of beer.
They likewise would have no clue you were charged twice for each item at the hypothetical store. All they know is the total. You could complain about the duped charges to VISA, but if the sale states you're going to be charged double, they can't help. It's not their fault the customer didn't read the sign.