That's not how salts work. The point is that an attacker can do a lot of effort in advance to generate a massive rainbow table containing the hashes of a large set of possible passwords (or in practice, simply pay for access to such a service).

By adding a random nonce (i.e. the salt) to passwords before hashing them, you force the attacker to include all possible nonce values in those passwords. For each extra bit in the nonce, you double the size the rainbow table, quickly making it infeasible to generate one.

So even if the salt is public, it will still do its job in preventing the use of rainbow tables. The attacker will be forced to brute-force by trying all possible passwords in combination with a given nonce just to crack a single password hash.