I agree with you about uniqueness, but being unique doesn't matter with respect to their claims.
Any educated person with sufficient math knows the mathematical structure of a hash will never be unique. Its a Galois field, or 'finite field' after all.
The core of this issue is the flawed but convincing belief promoted by an entire industry that if the probability is sufficiently low, its unique, and following these axioms if its unique its an individual person (eyeball).
Under that assumption, all you need to do is collect fields of information that are variable, and group them together such that it yields to a sufficiently low threshold, I think currently that threshold is about 1 per million. Its a very clever way to defraud advertisers if you think about it. You create an exaggerated market, and charge for each advertisement view.
In my opinion its just flawed thinking but there are some real fanatics out there that subscribe to this dogmatically.
For example applied probability is used as part of the protocol design when accounting for binary erasure channels in things like cell phones. You shouldn't be able to have communications blocked in only one direction, or altered without it being noticeable, but stingrays may have the ability to do this according to the limited documentation that has been released so far.
Probabilities in general have real problems fundamentally with validity. I think the most common approach today is the Axiomatic approach, or the Frequentist Approach, both have significant limitations and often devolve when self reference is indirectly introduced.
So I guess I'll ask, are you a believer?