The result isn't counter-intuitive to those familiar with fairly basic human neuroscience. When you close your eyes, for example, low frequency, long-range synchronization also increases.

The stated "counter-intuitive"-ness is more likely an artifact of the translation of the result to layman's terms, where the traditional (since the industrial revolution) way of thinking about the brain and mind is that it is a machine, and the function of this machine is consciousness. I think several such artifacts often appear in these sorts of articles on neuroscience.

If you wish to actually understand and interpret the results for yourself, without the crude and inevitably inaccurate lens of the science writer, you have to read some of the books written by neuroscientists themselves. Rhythms of the Brain by Gyorgy Buzsaki is the best I've read so far.