A more accurate analogy is "it's not his actual money, it's a link to a webpage or image that has his bank account and routing number."

My contention is that links to pii are themselves pii.

A name, Jon Smith, is technically PII but not very specific. If I have a link to a specific Jon Smith’s facebook page or his HN profile, it’s even more personally identifiable than knowing his name is Jon Smith.

That is crazy. The target of a link could change, which means that all links are Schroedinger's PII.

And if a link to PII is PII, then a link to a link to PII is PII, and thus all links are PII unless it links to the dark (unlinked) Web