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Arenamontanus comments on Anthropic signature: strange anti-correlations - Less Wrong
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This is incidentally another way of explaining the effect. Consider the standard diagram of the joint probability density and how it relates to correlation. Now take a bite out of the upper right corner of big X and big Y events: unless the joint density started in a really strange shape this will tend to make the correlation negative.
This is known as Berkson's paradox and it is ubiquitous. A lot of people have written about it and its implications, e.g. Yvain (underlying reasons why anti-correlations arise are very similar).