The dichotomy in the title is false. As the article states:
&quot;This observation fits together with studies that show the best way of maintaining mental harmony during mind-wandering is to be able to be aware of the fact that you are doing it.&quot; 
Which means, precisely, that it&#x27;s a state of mindful watching a stream of thoughts, without exerting any pressure or expectations of the result. 
With mindfulness you can do everything better, including thinking - the fact that you are aware of it doesn&#x27;t mean that you overly control or restrain it. You can let the thoughts flow freely when  it&#x27;s useful, you can stop them (with some practice) when it starts to be counter-productive.