I would argue that zero-knowledgeness is a property that (from an information theory perspective) can only be approximated. It is not possible to have a technique based on information theory that works like the example with the hats; you always give a tiny bit of information about the solution (this information is the hash in the commitment scheme), and this is kind of interesting.
Well, yes, but as long as you use a nonce and sufficiently large hash you can make the probability of brute forcing the hash arbitrarily close to zero. So it works well enough :)
