Earlier quoted context omitted.
Excuse me for my ignorance if incorrect, but if a unique salt is used for each user, and the salts were not compromised, would it then not be possible for the passwords to be cracked no matter what encryption is used?
Unique salts have to be stored somewhere. A common practice is to just use another piece of information associated with their account. The purpose of a salt is to make various bruteforcing attacks difficult. It doesn't do much if someone has full access to a system.
All absolutely true.
> It doesn't do much if someone has full access to a system.
Not true. Without salt they can try passwords and if the hash matches ANY in the system they know the password for those accounts. With a big dictionary of likely passwords (or just normal words) many passwords will be discovered very quickly.
With salt you have to try the password dictionary against EACH user (actually each salt value but they should be unique). This makes discovering passwords harder by a factor of the number of users. Yes you can pick any user and run the dictionary and have a good chance of finding the password but you have to expend large computing resource for little reward (possibly worth it to break a bank account but not the average web app).