Two exact templates, sidebar showing in one but not the other

Look at the config.php:

function roots_display_sidebar() {
  $sidebar_config = new Roots_Sidebar(
    /**
     * Conditional tag checks (http://codex.wordpress.org/Conditional_Tags)
     * Any of these conditional tags that return true won't show the sidebar
     */
    array(
      'is_404',
      'is_front_page'
    ),
    /**
     * Page template checks (via is_page_template())
     * Any of these page templates that return true won't show the sidebar
     */
    array(
      'page-custom.php'
    )
  );

  return $sidebar_config->display;
}

So if your home is not the front page the sidebar will be displayed. There is probably a way to adjust these settings per filter, but you can also just change the first array to …

    array(
      'is_404',
      'is_front_page',
      'is_home'
    ),

… to hide the sidebar.