Ah, you're right. Babbage's Analytic Engine was designed to use punch cards, and I totally forgot about the Hollerith Machine that I read about just last year. I wonder what other false information Poundstone's book has. Thanks for the heads up!
Not only did Babbage's Analytical Engine use punched cards, it was specifically inspired by the Jacquard Loom, as Babbage was a massive fan of it (and owned a portrait made on one!)