They can be public and they can be private.  This comes down to how the clients choose to implement them while following the specification.

- public association to pubkey, public clear text data
- public association to pubkey, private encrypted data
- public association to pubkey, with a mix of clear text data and encrypted data
etc

In the case of Corny Chat petnames, I went with making it known the relationship was public, but the actually assigned petname is private.