In theory, shouldn't CTR and organic traffic be closely (if not almost exactly) correlated?
Not necessarily as traffic can be 'direct' i.e. some one can come to the site by just typing in the URL, there are also situations were a refered visitor, can be read as direct by Google Analytics.
You're not totally off - since Google uses CTR as the one of the most important elements for determining changing rank for particular keywords - as your CTR grows, so will your organic traffic. That's why your meta tags and title tags as displayed in organic search are modified by Google; Google is trying to find the best display meta and title that increases your sites CTR.