My understanding: the rubberhose crypto-analysis, even if unsuccessful, will result in some major damage done. Determined attacker might try to apply it regardless of any online statements on the off chance that the statements are wrong.
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.
I still believe, which might indeed be naive, that this is the best way. It results in a failed mission lowering the risks for others and if applied for all theses services (again naive), in a general understanding.