That's a really bold claim. I fail to see any evidence of it.
Anecdotally, it's not true at all. A huge portion of my city dweller friends are miserable and constantly talk about quitting their jobs or moving. I cannot think of a single friend in the mountains who is as miserable. None of them want to move to a big city removed from nature.
Anecdotally, this is somewhat true for me. My wife and I moved to a rural location last year and every few of months we make a trip to "civilization" (e.g. a major city) to "recharge". Waking up every day surrounded in nature and breathing in the sweet air of a pine forest is great, no doubt. But being able to walk to a pizza shop or bike to a park are something we really miss too.
We're in bit of a pickle though, our daughter will be starting school in a couple of years but the public schools here are not very good. They have some of the lowest scores in the state and the state's scores are some of the lowest in the country...
I have mostly heard this from folks who have been there over a decade, often with young kids. Everywhere has its problems, of course; pick what matters to you.