Earlier quoted context omitted.
Er... "they" have also published the full source code involved (at https://github.com/mozilla/browserid ) and a privacy policy at http://www.mozilla.org/en-US/persona/privacy-policy/ that you can compare to said source code as desired, if you're using Mozilla's identity provider. As far as the architecture of the overall thing, there are also http://identity.mozilla.com/post/7899984443/privacy-and-brow... and http://…
Not even the links you posted tell me a) where certificates are stored and how they are protected, b) what measures are taken to prevent unauthorized use of those certificates by the ID provider, the browser (plugins?), other entities, c) how the act of entering an e-mail address is secure (other people may have access to my computer and know my e-mail address). Admittedly, I didn't watch the 1 hour presentation vide…
Assuming you're saying other people have access to your email account already, it's game over: practically every site will send password reset procedures on demand to the email you used to create your account.
Alternatively, if you're saying other people know your email address, that's not really relevant. They need to either be able to read email on your account (see above), or be able to implement an Identity Provider on your email domain.
If an unauthorized party is able to implement an IdP on your email domain you have an even worse problem: your email provider apparently is unable to control basic aspects of their own domain.
to actually implement an IdP, your email provider must publish a https://domain.com/.well-known/browserid file. If a rogue third party can do this at will, I'd say your email provider has horrible security and your security assumptions are probably broken anyway.