It's a nice design. But in this particular case, does it matter? What's the threat, that the credentials you enter into a fake basic auth box could be sent to the server? The credentials you enter into a real basic auth box are just sent to the server -- basic auth doesn't do any password hashing clientside. Why would a phishing site (that's pretending to be another site that uses basic auth) fake a basic auth box when they could just send the right header and get a real one?

What am I missing?