The only way I can imagine secret jail time working is by publicly charging that person with a crime they didn't commit to cover up the actual reason. This is similar to what is alleged with the CEO of Qwest, who would not cooperate with the NSA and was then charged with insider trading and is still in prison.
However, what possible reason would the person have to remain silent about the real reason they're in prison once they're already in prison?
He's jailed for 6 years, I'm sure most people believe it's because he's eeevil capitalist scum, and whatever the truth, everyone else in his position has to take it as likely they'd suffer the same fate.
Now that this seems to have turned a corner it might play out differently, but "Do you feel lucky, punk?"
However, what possible reason would the person have to remain silent about the real reason they're in prison once they're already in prison?