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Lumifer comments on Why the tails come apart - Less Wrong
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"At the extremes, other factors may weigh more."
Nothing that hasn't been said before, and in my opinion better.
I don't particularly like your "ellipse" generalization, either, because it's just wrong. We already know a perfect correlation would be linear. We already know a lesser correlation is "fatter". Bringing ellipses into the issue is just an intuitive, illustrative fiction, which I really don't appreciate very much because it's not particularly informative and it isn't scientifically sound at all.
Please don't misunderstand me: I do think it is illustrative, and I do think it has its place. In the newby section maybe.
Understand, I am aware that may come across as overly harsh, but it isn't meant that way. I'm not trying to be impolite. It's just my opinion and I honestly don't know a better way to express it right now without being dishonest.
I think you're mistaken about that. An ellipse is the shape of a multivariate normal distribution, for example. In fact, there is the entire family of elliptical distributions which are, to quote Wikipedia, "a broad family of probability distributions that generalize the multivariate normal distribution. Intuitively, in the simplified two and three dimensional case, the joint distribution forms an ellipse and an ellipsoid, respectively, in iso-density plots."
That's a meaningless phrase, correlation is linear by definition. Moreover, it's a particular measure of dependency which can be misleading.