The user is not asked for his credentials because the Facebook authentication cookie is still present in the WebBrowser
control.
So to completely logout the user from Facebook, you need to clear the WebBrowser
cookies.
Unfortunately, there is no easy way for erasing cookies on Windows Phone 7.
On Windows Phone 8 you just need to call ClearCookiesAsync:
await new WebBrowser().ClearCookiesAsync();
Here is a tutorial that makes use of it: http://www.developer.nokia.com/Community/Wiki/Integrate_Facebook_to_Your_Windows_Phone_Application