"We hash passwords with a one-way hashing algorithm, with multiple hashing iterations and individual salt per password."
Bluntly, for a user of a site like this in 2017 there is simply no excuse for sharing passwords. In ops we used to say "If it's not backed up, it doesn't exist" - and I think a modern corollary could be "if your password isn't unique per site, then no, it's not safe". If you reuse passwords, your security is only as good as the weakest site you used it on, and you are playing with fire.
Just go and buy 1password (or similar) and use it.
If your username is...
Based on that statement it sure doesn't sound like the PWs were salted (or at least properly salted).
That's because the user specific salts were probably in the same db. This will make it difficult since a brute force attack must be done for every single password. But it is still not impossible.
Even if the salts aren't unique, can you explain how can they use the hashed password anywhere?
If I give you a hashed password and the salt used, what exactly can you do with it? (apart from brute forcing)
A password DB breach, salted or not, allows an offline, non-rate-limited, attack on those passwords.