Storing password in tables and Digest authentication

Question

The subject of how to store web site users passwords in tables has come up several times on SO and the general advice is to store a hash of the password, eventually an HMAC

Answer 1

The reason I am using pre-computed hashes is not protection against attacks, but to secure users privacy.

Attacker can indeed authenticate, but he cannot (easily) see password of my precious users and compromise other services they are using etc.