Earlier quoted context omitted.
It can work the same way. You just slowly figure out the hash: this pw for this user was a bit faster than all the other failures, so we know the first byte of the hash is ... If you have a bunch of hashes precomputed, you can start to figure things out pretty quick. The point is it's still leaking information about what's going on.
This makes sense, I hadn't thought of knowing the hashing method and it being unsalted. Knowing those it would be just as easy to whittle the list down exactly the same way.
You may then argue that you can have the value space of all popular passwords, but that isn't going to be any more effective than just trying all of the possible passwords.