Facebook Connect requires you to create a new facebook app for logging in and authentication, so you really are not “out of facebook”. When you add facebook initialization code:
FB.init({ appId: AppID, status: true, cookie: true, xfbml: true });
and facebook connection code:
<div id="fb-root"></div> <script src="http://connect.facebook.net/en_US/all.js"></script>
You link your application with facebook. If something in your facebook application is incorrect (application identifier, website URL or canvas URL in your facebook application), then the application will not work. And all incoming calls, for example, will cause an error.
Do not think of it as a completely separate entity from facebook. The application is very well connected with facebook.
Try making a facebook application using a connection. Then you can see which scripts are attached to the root and connect the script. This may give you a better idea of what is happening (there is a lot)
More info from facebook / developers here
This page may also be useful.
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