I still assert it's only a matter of cross-correlating that data with something else.

I don't know what kind of data you're working with, but for the sake of example let's assume you're handling buying records from supermarkets. You obviously hashed people's ClubCard/credit card numbers. But let's say I get hold of the data from an ALPR on a street near one of the markets. Would correlating that with your database not help to deanonymize a lot of your data?

My point is - as the data collection of every kind increases, for every dataset you have anonymized, there will be a lot of other data sets of all sorts that can be used to deanonymize back yours.