I would consider a salt to be a "quasi-secret" that doesn't need to be treated with extreme care, but should probably not be posted in public or something. If the attacker knows the salt, he can start building tables before he attacks you, even though it's unlikely that he could get very far with that anyways.
Sometimes salt is used a quasi-secret but that is generally bad practice. A good crypto system is one where you can assume the attacker knows the alogorithm, the salt, the ciphertext/hash, and other details (like number of rounds) and still never be able to crack the secret.
If the attacker knows the salt, he can start building tables before he attacks you
The purpose of the salt isn't to prevent an attack. It is to prevent the attacker from building a general solution.
For example SHA-256 of password is:
5e884898da28047151d0e56f8dc6292773603d0d6aabbdd62a11ef721d1542d8
however the SHA-256 of "password|192386633" is
dc8b776a57bff42900f4c4e345731d4c2addeae4df957c45b06a6c8450cd612a
The 192386633 isn't intended to make the passphrase stronger. That is the purpose of the passphrase. The 192386633 is intended to make the hashing of passphrases useless for any other purpose than a specific attack. Even known the salt serves this purpose.
Someone who feels that the salt needs to be non-public is either:
a) uninformed
b) feels their passphrase may be weak and is trying to compensate by adding more entropy via the salt
It is possible to produce secrets which can't be brute forced even when the salt is known if the following are true:
a) an algorithm which slows the throughput of attacker is used (single round SHA-256 is not secure for protecting passphrases)
b) a random salt of sufficient length is used (at least 64 bit but 128 bit is better)
c) a strong passphrase is used
Just remember to use strong passwords if you go the "brainwallet" way!