How to prevent a user from updating other users in WordPress?

I’ve implemented my “dirty” solution as follows. If there is an better or cleaner approach, feel free to provide an answer:

function stop_access_profile()
{
  global $pagenow;
  if ($pagenow != 'user-edit.php') {
    return;
  }

  $user_id = get_current_user_id();
  $profile_id = intval($_GET['user_id']);

  // Some logic implementation to decide whether the current user can see the current profile
  // Omitted since it's irrelevant 

  if (!$can_see_profile) {
    $profile = get_user_name($profile_id);
    wp_die("You aren't allowed to see or edit the profile of {$profile}.");
  }
}
add_action('admin_init', 'stop_access_profile');

It’s not relevant but the get_user_name is a utility function that I wrote:

function get_user_name($id, $default = "")
{
  if (!isset($id)) {
    return $default;
  }

  $user = get_user_by('id', $id);
  return $user->first_name . " " . $user->last_name;
}