A reasonable expectation would be that Amazon doesn't know about the Facebook post, that Facebook not know about the Times subscription... etc.
Replace the left side of the expression with "Google" and you'd have what most users might expect from Incognito. That is, that Google not know about the Amazon purchase, Facebook post, or Times subscription. That Google does know, essentially, even from Incognito, is the problem.
But Google doesn't know who you are when you're in incognito. They famously "don't do fingerprinting".
Of course, if Amazon or Facebook or the Times tell Google or at least hire someone to figure out who you are and tell Google then it's surely not Google who is tracking you.
And likewise, if Google Tag Manager and Google DoubleClick Ads make it easy to add and integrate with the one or two missing pieces from third parties to make this work, then it's not Google's fault either.
I was sticking with the analogy established in the post I was replying to. To me they are variables in the pseudo-code, for the purpose of understanding the algorithm, not the actual underlying reality being discussed.
Right, but GP picked those variables intentionally, as things that Google doesn't (can't) track. If, for example you replaced "Amazon" with "Google", well you'd obviously expect Google to have the data.
So then if you replace "Amazon" with "company that subcontracts to Google for analytics", you'd still expect Google to have the data.
Replace the left side of the expression with "Google" and you'd have what most users might expect from Incognito. That is, that Google not know about the Amazon purchase, Facebook post, or Times subscription. That Google does know, essentially, even from Incognito, is the problem.