Then, the next time I went to use my card, it was blocked. I called the bank again and spoke to someone new, who informed me that the original calls had been legitimate - they had the same reference number and everything - and the card had been blocked due to lack of response!
Obviously a false positive on the scam detector is less of a problem than a false negative, but was still pretty incredible. No idea what was with all the people talking about being scammed from that number online; I can only assume that they (like the first rep) assumed it was a scam, since if the bank needs to call you, they should tell you to call back using the number on your card, not some random number they give you. But apparently that's exactly what they did.