Yup, people tend to confuse concepts and refer to synthetic data as anonymised data. They are very different things.
Anonymised data or redacted data are transformations of a data set that _hopes_ not to leak too much PII / sensitive data. People don’t use ML to anonymise but they do use ML to classify as a first step before splatting or generalising.
In that case, its absolutely right that the ML classifier not being 100% results in PII leaking.
This is a key reason why anonymisation and redaction are widely seen as problematic and are being replaced by synthetic data and, maybe in future, homomorphic encryption.