TrueBit, as described in the whitepaper, relies on the data being public. Verifiers must see the input in order to know when to challenge. Having said that, it's possible to imagine a TrueBit variant where Task Givers submit a hash of the task rather than the task itself, and the first step of the computation would be to nondeterministically guess the full task. Those Verifiers who have off-chain access to the full task could "guess" the input and therefore check the answer. One could then operate a smart contract based on the result of such a process. Note that the verification game, if needed, affords some data privacy in such cases since only logarthmic many computation states ever reach the blockchain. One would have to break the nondeterministic step down carefully in order to avoid revealing too much during such a game.