Dave Brin's answer: privacy is lost, but we should make sure that it is lost by all equally. We must eliminate all avenues that grant privacy to any class that is otherwise favored.
Is it personal if it can be inferred? When your water is used, electricity is used, internet is used, vehicle is used, all require use of infrastructure belonging to a second party, therefore the information from it is not just seen by you.
My impulsive response is that any data from which identity can be inferred is PII.
I'm not smart enough to understand the maths of differential privacy. I gather that it's a calculus for determining how much to fuzz the data (points) to anonymize. So car rentals may need to decrease the accuracy of both timestamps and locations to create hash collisions with other rentals.
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Maybe there's a way to create logical "data diodes", for lack of better term, for the notion of data flows and relationships go only one way. So for electricity, each meter has GUID, which is never referenced directly, meaning any external reference (foreign key) references an opaque identifier which can then be dereferenced within the system. Then anything referencing the meter will be issued its own opaque identifier, so that no two references can be linked from outside the system.
I'll have to dig out my copy of Translucent Databases to see if I'm making this up or repeating something that author had already thought through.