When you install the Payburner Wallet browser extension you will receive a scary warning about the permissions the extension has requested. First and foremost, Payburner does not, in any way shape or form, transmit and store externally information about the websites you visit. No, never, will never! And, in fact, we do not even machine read or parse the content of your websites.
Why then?! We do this, in order to allow any website to interact with the Payburner Wallet in a secure manner to perform activities like request payments and login to the website with the Payburner ID. And note, even if the website makes these kinds of requests (and others in the future), you remain in control. The Payburner Wallet won't do anything unless you explicitly tell it to.