Briefly, the idea is that city environments make it harder to focus and to maintain self-control, and that even a little nature helps.
This studies doesn't explain why some people *want* to live in cities, nor does it address that a lot of people seem to want some nature, but then they want to get back to a city. Nor do they address the possibility that cities are good for many people from about 17 to 30, even if they're rough on younger and older people.
The bit I found most interesting was about parks working best if they have a variety of plant species-- my favorite park is only a half block. (More or less at 8th and Fitzwater.) It isn't big enough to supply any protection from noise. I'm tremendously fond of the big planters that have a bunch of different sorts of plants growing in them.
Link thanks to supergee.
Addendum:: My point wasn't "Why would anyone want to live in a city?". It was "those researchers (or possibly the popularizers) aren't looking at a really basic question".
siderea and atomicat point out that if 'nature' feels that safe, it's been remade by and for people. Actual nature, the place we evolved in, is a good bit more dangerous.