This is obviously true, as you are stating an axiom. But what I think the grand parent is trying to say is that databases with PII can often be deanonymized by looking at the other data that isn't obviously PII.

Take for example a database over all mobile phone positions over time, this can be 'anonymized' by removing all connections from the phones to information on who owns the phones.

But it can still be trivially deanonymized by analyzing where the phones are at night and during office hours, not very many persons work in the same building and sleep in the same house.