"any information relating to an identified or identifiable natural person (‘data subject’); an identifiable natural person is one who can be identified, directly or indirectly, in particular by reference to an identifier such as a name, an identification number, location data, an online identifier or to one or more factors specific to the physical, physiological, genetic, mental, economic, cultural or social identity of that natural person"
Pseudonymization (separating unique identifiers from the rest of the datapoints) can and should be used as a safeguard, but doesn't remove the need to protect the data, particularly if you keep a link between the two.
I didn’t say it was. The original conversation wasn’t about PII it was about anonymising. Fingerprints defeat anonymisation.
I reckon in practice with for example an Amazon sales log with names removed and my public Twitter feed you could de-anonymise me with a high degree of certainty.
This isn't going to make you GDPR compliant by itself but it's a start.