There isn't anything special or harder about an all zero hash.

If you ask me, "will you bet your life on the fact that no SHA-256 hash will be found by 2020 with a value of 00000000000000000000000000000000000000000000000000000000000000000, without SHA-256 being broken?", I'll say "sure", because this has a probability of about 1 in 10^50, and will thus not happen.

If you ask me the same about b0867d52439eedac556187087c69bbe6fdb3c47f266780775931068f18fae223, I will refuse. Why? Because I don't know how you came up with b0867d52439eedac556187087c69bbe6fdb3c47f266780775931068f18fae223. Maybe you generated it truly randomly (and then the answer is the same). But maybe you came up with it by calculating some SHA-256 hash, and then I will lose even before the bet began.

What makes me so confident in the 00000000000000000000000000000000000000000000000000000000000000000 case, and not in the b0867d52439eedac556187087c69bbe6fdb3c47f266780775931068f18fae223 case, is that 0 has a much lower Kolmogorov complexity (and the describing program has no reference to anything remotely relevant to SHA-256).