Lot of comments about meditation here. The thing is, most forms of meditation are active -- for example, pay attention to your breath. Presumably at least some of the mind wandering that went on in this study was about the material, and most (though not all) forms of meditation would suppress that.
My takeaway from my thus far limited experience practicing mindfulness meditation is that (at least that particular form of meditation) it is not about suppressing thoughts. It's not about actively quieting the mind. Rather, it's about becoming an observer of the thoughts in your mind, rather than the active participant you usually are. You view your thoughts as if they were just another sense from the external world. i.e. you become a passive observer.
So, at least mindfulness meditation, is passive. And that's a rather popular form of meditation these days. It may have the same effects the article discusses, as a result.
(NOTE: The focus on breath during mindfulness training is temporary, and is really just a technique to get you to A) relax and B) begin to focus on the present and sensations you don't normally observe).
I have seen other people who have this conception of meditation, but I am not sure it paints the whole picture. Among the different schools of meditation there are both those that tend to "suppress thoughts" and those that simply observe whatever arises.
In the first category I would put techniques which teach you to focus on a meditation object, most often the breath or a mantra. If someone says "mindfulness meditation" I generally think they are referring to this kind of meditation, and examplars can be found in books like Mindfulness in Plain English or The Mind Illuminated (even though there are also both quite different approaches to meditation, one being focused on "insight" first and the other based on "concentration" first). They don't teach you to suppress thoughts, but they teach you to focus on a particular thing and IGNORE thought, which has the effect, long term, of causing those thoughts not to arise.
But there are also schools that focus on "open awareness" or "just sitting" styles of meditation. This is very common teaching in Zen Buddhism but is also practiced in some schools Tibetan Buddhism, at least in Dzogchen. This, I think, is what you are referring to; where you sit and observe at a mental distance whatever thoughts arise. Eventually, this also causes thoughts to arrive much less frequently.
If you are referring to the research literature, however, I think mindfulness generally refers to the first kind. As with everything, the borders blur together.
This is true; genuine mindfulness does not suppress thoughts. Thank you for clarifying.
In practice, most beginners (a phase that can last for years) find it much easier to use an attentional anchor like the breath. Even advanced practitioners can find great benefit in such a practice.
As long as one understands these nuances, then yes, it is possible for "mindfulness" not to interrupt the natural learning process that can take place when we rest.
I also like the mindfulness approach of Ellen Langer, who recommends active observation of surroundings, which has a side effect of quieting the mind and providing the same benefits (for me at least) of breathing-focused mindfulness meditation. Almost like a shortcut right to your point B.
"Mindfulness, she tells the medical school audience, is the process of actively noticing new things, relinquishing preconceived mindsets, and then acting on the new observations. Much of the time, she says, our behavior is mindless."