You might say that there would be other person names and places in mentioned in the records and from that network and timeline you may be able to deduce the identity.. but these PII can in turn be depersonalised. And also this is not scalable for widespread damage.
It just need a bit of thinking when designing a system. Frankly any org that ask for PII and doesn't have a well thought out way to store them should be heavily penalised.
That's what the law should do standardised methods of storing sensitive data.