Protect AppListItemList Add/Remove and fix sync bugs

ui/app_list/app_list_item.h

Index: ui/app_list/app_list_item.h
diff --git a/ui/app_list/app_list_item.h b/ui/app_list/app_list_item.h
index 69139ebf2e75d810a9b8abef18728dd3898abb62..de67a793a9d564260dc2f48ab4420c3cf8375846 100644
--- a/ui/app_list/app_list_item.h
+++ b/ui/app_list/app_list_item.h
@@ -22,6 +22,7 @@ namespace app_list {
 class AppListItemList;
 class AppListItemListTest;
 class AppListItemObserver;
+class AppListModel;
 
 // AppListItem provides icon and title to be shown in a AppListItemView
 // and action to be executed when the AppListItemView is activated.
@@ -73,6 +74,7 @@ class APP_LIST_EXPORT AppListItem {
  protected:
   friend class AppListItemList;
   friend class AppListItemListTest;
+  friend class AppListModel;
 
   void set_position(const syncer::StringOrdinal& new_position) {
     DCHECK(new_position.IsValid());