I think the OP misunderstood the guidebook.
The OP said
According to (12) it might seem that the distribution of prime numbers can only be a matter of knowledge, never of opinion. Obviously that is false.
Is the distribution of prime numbers not fully understood and is that the reason why the quote says that one can only have an opinion? The ...
From an initial analysis, your acquaintance is essentially putting forward a hypothesis about axiom selection; underlying this is the following premise:
What I know depends on what axioms I take.
I'm interpreting this premise as a claim that we as humans are doxastically axiomatic, by which I mean that it works something like knowledge based systems (KBS); ...