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Douglas_Knight comments on Why the tails come apart - LessWrong
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That isn't an explanation, but a stronger claim. Why should it form an ellipse?
A model of an independent factor or noise is an explanation of the ellipse, and thus of the main point. But people may find a stumbling block this middle section, with its assertion that we should expect ellipses. Also, regression to the mean and the tails coming apart are much more general than ellipses, but ellipses are pretty common.
It is regression to the mean, as you yourself say elsewhere. I'm not sure what you are trying to say here; maybe that people's vague worries about regression to the mean are using the technical concept correctly?
Multivariate CLT perhaps? The precondition seems like it might be a bit less common than the regular central limit theorem, but still plausible, if you assume x and y are correlated by being affected by a third factor, z, which controls the terms that sum together to make x and y.
Once you have a multivariate normal distribution, you're good, since they always have (hyper-)elliptical envelopes.