Someone who pushes the "nothing to hide" argument probably wouldn't understand the implication of your response. I suggest a different approach: say "Okay, in that case what prescriptions are you taking, how much money do you have in your bank account, and how often do you have sex? After all, you have nothing to hide right?"
That also puts them on the defensive side of the argument.
For some people, no. I tried to cover several different bases, but you get the idea: ask sensitive personal questions. Maybe the money one should be about credit card debt.
That puts them on the defensive. Since now they have to justify their fear for the unknown. And then we're onto the real topic: fear.