Using 'Primary links' for your Drupal site's main navigation menu is a great idea. However, most themes by default display primary links in such a way that if the menu has sub-child menus, they will not be displayed. Fortunately, the solution is much easier that you'd think.
First off, the way that most themes generate primary links is like so:
theme('links', $primary_links);
As mentioned, this will only output the top-level menu items, like so: