It's changable. We don't sync with FB afterwards, though we likely will need to sync email address changes. (Which could turn into a bit of a nightmare if you switch to an email that is connected to another account)
Well, as an FB-registered user, you don't actually have a password. So you can't change your email or your password (since there's nothing to verify against). The interface doesn't show this yet. (If you have access to the email address, you can do the lost password thing and that will generate a password for you, though that's roundabout.)
Thus, if you change your email in FB, we really need to change your email here to ensure it's linked correctly.
No, I'm not sure why you would want to though - there's no difference in the accounts, except for the password thing... and really, there's no secure way to give you a password except via a lost-password-esque system (since we can't re-verify your credentials).
I'm talking about registering the regular way where you pick out your own password. I'm not wanting to do this, mind you, I was just using me as an example.
But someone is bound to ask this in the future.
It's an FB association issue. We don't get a password from FB; we just know that you authenticated. But changing things like passwords and email addresses need confirmation of your existing password (try it on FB, for example). However, FB offers no "authenticate again, and check their password" system, so we can't give you a password or let you change your email through that. The only way around that is to email you a temporary password, as we know you have control of that email address (a la lost password).