In the article they point out that anything that can be used to identify one click and link it to a subsequent click - in your example the cookie - is considered person hall data. This is because you may be able to de-anonymise a person from the pattern of their interactions.
The cookie is the same for all users. There is no value unique to each user. All that is logged is “a visit to this page occurred at X time” and if the request contained the cookie then it is marked “unique”. The cookie value is the same for everyone.
What should matter is what’s logged. Every request contains an IP that’s how the web works.
Ah yes - I misread your suggestion. Seems feasible in that case.