And you really think that people who routinely use torture to extract information, and for whom claims that "I don't know it!" is basically the standard obstacle to overcome, will just believe him without even trying, because it's "math" and therefore true?

The reality is, in the xkcd Rubberhose cryptanalysis scenario, being actually unable to give up the information is a MUCH WORSE situation to be be in than having a key to give up before they permanently maim/kill you. It might be better for a third party who benefits from the information remaining secret, but not for the person unable to divulge it.

But thinking you're safe because the attackers will read, understand, and believe your claims of uncompromisable cryptographic security is dangerously naive.