This is of a kind with several other very successful de-anonymization efforts in the past few years.

There's probably some clever way to express the general problem in information theory terms and prove that any set of data with certain characteristics must be de-anonymizable to some given extent. 6 billion people in the world is still just about 33 bits to uniquely identify an individual (and of course generally we're not talking global population), and so even a very small number of bits that can be correlated back to the real world in arbitrarily clever ways will reveal real-world identities in a putatively anonymous data set. It wouldn't take much to clean that up into a mathematically rigorous statement; no matter how you slice it, low tens of bits will tend to identify people and that's a low threshold.