Apple makes some bold claims about how they respect user privacy and don't create profiles across their whole system.

Could there be bugs in that causing it to be imperfect? Sure.

Could they just be deceiving their customers? Very unlikely given the number of employees who would need to collide in such a fraud.

Asking Apple to open their systems to enable this to be audited is as reasonable as asking Google to open-source the search algorithm so it can be audited for political bias.

Are you calling for that too?

And just to be clear - Google doesn't make any claims about not creating a detailed identifiable profile on each user, incorporating all the data across all their services as they see fit.

If you are going to accuse Apple of lying, the burden of proof is on you.