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.
That's ignoring the fact almost nobody will accept having to keep track of an "alphanumeric ID" to get treatment.
This may not be the status quo of the medical system. But I'm willing to bet it wasn't conceived and put in place when breaches like this could happen frequently and the consequences were damning. Overhaul of the process is required. Just keep paying the Ransom/Hackers is not the only and meaningful solution.
John Doe | Street 1234 | Therapy | 6 Units | $12,367
That is way less interesting information than what we are discussing here...
A lot of detailed information is often required for the payer to green-light the actual treatment, at least in Germany.
Ideally the payer also wants/needs to keep track of what was already done and for what reasons.
Even if you keep all of that to a minimum, you still end up with a fair bit of meta-data that allows for rather detailed insights.
It turns out this is not as easy as you think it is.
Now the doctor is unable to verify the identity of the patient.