Surprising that no mention is made of rainbow tables or lookup tables. If you hash something that can easily be looked up in a table, it's obviously not anonymous.
Passwords are stored as salted hashes for these obvious reasons...
In the case of salts, the article admits "Don’t get me wrong, this does make it significantly harder to attack a leaked database to unmask every user..."
So salts definitely do help. And if you chose your salt well (e.g. global fixed/rotating plus local/temporal) you significantly increase your protection compared to not using a salt at all.
Passwords are stored as salted hashes for these obvious reasons...