A man with a crowbar won't continue to beat you for your password if you can prove that you can't divulge it, unless he is beyond the reach of logic. At that point he might as well be beating you because he doesn't like the color of the moon, and you would best get together with some of your friends and divest the lunatic of his crowbar.
But there is a logical reason to beat you for the password you can't divulge, namely to serve as an example and deterrent to any future persons who might attempt to restrict access via the same mechanism.
