Earlier quoted context omitted.
If the password is hashed well, with stretched SHA1/SHA256 or (better yet) bcrypt, then yes: breaking the hash would involve a significant advance in cryptography.
hm? I'm trying to say that once you have the hash, you can run a dictionary attack against it without any advances in anything. I can use whatever procedure the server uses to verify logins, and just try passwords. You can make the dictionary attack more expensive by using an expensive hash like bcrypt, but that's going to slow down your app, too. (http auth re-authenticates every page load.) so really, you can't mak…
The point of adaptive hashing is that doubling the cost of the hash on the serverside adds negligable overall cost, but doubling the cost of the hash on the attacker's side doubles their cost. This is not a complicated tradeoff.