fbconnect_invite_accept function does not allow call other hooks implementations as hook_invite_accept and even more serious the hook_user_insert, when a invitation is Accepted this function (fbconnect_invite_accept) is invoked and then drupal_goto (redirect to frontpage) and does not allow call other hooks implementations for other modules as hook_user_insert and hook_invite_accept.

My recommendation if possible is remove drupal_goto in fbconnect_invite_accept function:

<?php
function fbconnect_invite_accept($inviter) {
  module_invoke('rules', 'invoke_event', 'fbconnect_invite_accepted', $inviter);
}
?>

Juan