Ah! Right. There is no Persona password if your email provider supports Persona natively. If your provider has native support, you only authenticate with them, and the site you're logging into sees a credential issued by your provider. Mozilla is completely out of the transaction in that case.
You can try this yourself with a demo identity provider we have at http://eyedee.me/
Mozilla hosts a verifier as a convenience, but you don't have to use it.