After reading the post, I would rather phrase the key insight as: in the proposed protocol you don't have to reveal the nonce that hashes to the low value; rather, you prove you have it, thus destroying the connection between the nonce and the pool, so a solution can go out without any pool member being able to say "hey -- that was ours!"

This destroys the ability of pool members to trust that their nonces, where valid, will actually be used to claim a reward for the pool.

I'm not familiar with the work, but I assume there are validated zero knowledge proof protocols that prove you know a partial hash inversion of a particular quality, like the Pinocchio one referred to.

Edit: with that said, I don't agree that eliminating mining pools is a good thing; that just rewards those who can enforce cooperation by some other means (say, having the capital to personally run the farm), which has a far more unequal distribution than mining pools.