[elcct]

Alice has created a file containing random data. Authorities think it is an encrypted volume and wants Alice to give up the key. Alice has no way to prove it is just a file with random data and is imprisoned indefinitely for essentially having a file with random data =]

[heptathorp]

Mallory has created a file containing random data and planted it on Alice's drive. Then Mallory phones in an anonymous tip to the police...

[type0]

Nice, even in times of Stalinistic oppression things weren't as easy...

[amelius]

So typing the simple command

    cat /dev/random > filename 

can actually get you imprisoned. Good to know.

[triplesec]

Alice is able to switch the tracks on a trolley hurtling towards the encrypted only copy of the rest of her key towards a track where Clive, the only person who knows the key to that secondary encryption, is tied...

[pdpi]

Interesting thought experiment, but ultimately flawed. For this to make any sense, you first need to answer a question: Why are the authorities looking at Alice's computer in the first place?

Also, it's extrapolating a lot from a case that's actually a fair bit less sinister than what you're suggestion. Facts of this particular case here are that:

  1. The guy was a suspect to begin with, and they had
     enough evidence of him doing something wrong (from
     the Usenet side of the operation) that they got a
     warrant to search his computer.
  2. The disks are encrypted with off-the-shelf OS-provided
     full-disk encryption, which is relatively easy to verify,
     rather than some "purely random data that might or might
     not be encrypted".
  3. At no point has he denied having access to the keys (at
     which point it would essentially stop being a 5th amendment
     case).

Now, I'm actually of the opinion that he should _not_ have to decrypt those disks, but that's strictly a fifth amendment thing, rather than the more convoluted scenario you're suggesting.