The dichotomy in the title is false. As the article states: "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." Which means, precisely, that it'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't mean that you overly control or restrain it. You can let the thoughts flow freely when it's useful, you can stop them (with some practice) when it starts to be counter-productive.