It very easily could have been an honest mistake. A lot of receipts aren't carbon copies anymore, so if that's the case here, I'm not sure what difference it would make if you had kept yours.

As everyone else has mentioned, call the restaurant. Most managers will bend over backwards to keep customers happy, often at the expense of their staff, even when they know the customer is wrong. You know you're not, so it shouldn't be much trouble for them to fix it.