In this interview posted on Krebs on Security, this question was asked and answered:
BK: I’ve heard people say, you know this probably would not have happened if LinkedIn and others had salted the passwords — or added some randomness to each of the passwords, thus forcing attackers to expend more resources to crack the password hashes. Do you agree with that?
Ptacek: That’s actually another misconception, the idea that the problem is that the passwords were unsalted. UNIX passwords, and they’ve been salted forever, since the 70s, and they have been cracked forever. The idea of a salt in your password is a 70s solution. Back in the 90s, when people broke into UNIX servers, they would steal the shadow password file and would crack that. Invariably when you lost the server, you lost the passwords on that server.
Ptacek doesn't really explain why this is the case--he only says that salt has not prevented this type of attack in the past.
My understanding is that salt can only prevent pre-computation of password hashes because of the space needed to store the precomputed hashes. But if you have compromised the system, you will have both the salt and the hash. So the time to dictionary attack the hash does not change significantly (just an extra concatenation of the salt to the dictionary word).
Is my understanding correct?