Code from demo page, where it work well (change first checkbox to select).
I tried in Setting, Post and Page, default value in group not working, without group field it work as expected.

  piklist('field', array(
    'type' => 'group'
    ,'field' => 'checkbox_list'
    ,'label' => __('Group Lists', 'piklist-demo')
    ,'list' => false
    ,'fields' => array(
      array(
        'type' => 'radio'
        ,'field' => 'checkbox_list_1'
        ,'label' => __('List #1', 'piklist-demo')
        ,'label_position' => 'before'
        ,'value' => 'third'
        ,'choices' => array(
          'first' => 'First Choice'
          ,'third' => 'Third Choice'
        )
        ,'columns' => 6
      )
      ,array(
        'type' => 'checkbox'
        ,'field' => 'checkbox_list_2'
        ,'label' => __('List #2', 'piklist-demo')
        ,'label_position' => 'before'
        ,'value' => 'second'
        ,'choices' => array(
          'first' => 'First Choice'
          ,'second' => 'Second Choice'
          ,'third' => 'Third Choice'
        )
        ,'columns' => 6
      )
    )
  ));