Print the WHOLE menu? Is there a way to print out an array of the entirety of a menu in Drupal 7?

For example, I have access controls in place so that a user gets a role after they take a quiz, which then allows them to see the next quiz. So until they pass quiz #1, their menu will not show them any evidence of quiz #2's existence.

What I want to do is print out the titles of ALL menu items, regardless of whether the user has access to the associated nodes or not. I plan to rewrite the menu to make the permitted items links, while the others appear greyed out until the user gains access to them. 

I have not been able to find any modules, and simply doing this:

print_r(menu_navigation_links('menu-program-menu'));


only shows the items that the user has permission to view. 

Is there a module already that does this, that I just haven't been able to find? Does a query have to be made directly to the database or is there a way to do this with more finesse?
What you can do is to select corresponding titles from the database directly:

$sql = "SELECT l.link_title FROM {menu_links} l WHERE l.menu_name = :menu_name ";
$result = db_query($sql, array(':menu_name' =&gt; 'menu-program-menu'));
foreach($result as $object) {
    print $object-&gt;link_title;
}