Facebook Multi Friend Selector Doesn't Render (iFrame application)

I have an iframe Facebook application (using Facebook's new JavaScript API) that needs to allow the user to invite their friends to the app after entering a contest. I have the following markup in a div on the page (application name and Canvas Url redacted):

<fb:serverFbml>
    <fb:request-form
        method="POST" 
        invite="true" 
        type="{Name of My Application}" 
        content='Your text goes here. %3Cfb%3Areq-choice%20url%3D%{a url-encoded link to my Canvas URL}"/>' 
        label="Authorize My Application"> 
        <fb:multi-friend-selector showborder="false" actiontext="Invite your friends to use My Application.">
        </fb:multi-friend-selector>
    </fb:request-form>
</fb:serverFbml>

From what I understand, if you need to use FBML tags in an XFBML/iframe app, you just drop them into an fb:serverFbml element and Facebook takes care of it. Sure enough, my first impressions seem to be false. Instead of dropping in the form, I just get an empty white box, with the fbml seemingly untouched.

The design of this application assumes (probably incorrectly) that I don't need to authenticate the user to let them invite their friends. Is there a way to accomplish this, or do I need to require them to log in first? Facebook's documentation is (of course) vague on this.

EDIT: My FB.init() as requested:

$("body").prepend("<div id=\"fb-root\"></div>");
FB.init({
    apiKey: "{My apiKey is here}",
    appId: "{My appId is here}",
    status: true,
    cookie: true,
    xfbml: true
});

Solution

Ok, I got it to work. Here is how it looks for me :

<fb:serverfbml>
  <script type="text/fbml">
      <fb:fbml>
          <fb:request-form action='my_url' method='POST'
          invite='true'
          type='Poll'
          content='This is an invitation! <fb:req-choice url="my_url" label="Accept and join" />  '>
          <fb:multi-friend-selector showborder='false' actiontext='Select friends to send the poll' cols='5' rows='3' bypass='cancel' max="8">
          </fb:request-form>
      </fb:fbml>
  </script>
</fb:serverfbml>

and the JS injection code looks like this :

<div id="fb-root"></div>
<script>
  window.fbAsyncInit = function() {
    FB.init({
      appId: 'YOUR APP ID HERE',
      status: true,
      cookie: true,
      xfbml: true
    });
  };
  (function() {
    var e = document.createElement('script'); e.async = true;
    e.src = document.location.protocol +
      '//connect.facebook.net/en_US/all.js';
    document.getElementById('fb-root').appendChild(e);
  }());
</script>

So,

1) You dont need your APP KEY, only your APP ID in the JS code.

2) The XFBML needs to be wrapped inside a SCRIPT tag.