The bank can claim that all it wants, but this whole idea of "I didn't read the contract I signed" has never been a valid defense. Even in the case of those online Terms of Use, only recently has anyone been able to get a court to agree that they're even slightly unreasonable. But a physical contract like this? Sure, you can say, "I didn't read it", but the judge will just say, "You probably should have." and rule against you if that's your only defense.
You're right that "I didn't read the contract" is an invalid defense in the general case. However, this is an unusual situation. The peculiar circumstances would likely lead the bank to believe they were signing a different contract which they had in fact read. And there is (arguably) some willful deception on the customer's part.
In other words, it's not just carelessness on the bank's part. That alone would not be a sufficient argument. Rather, it's carelessness coupled with the customer's willful exploitation of that carelessness. That may be enough to tip the scales in the bank's favor.
