In this book, Diamond does what I think is a very good job of explaining all of his evidence. That is, however, not the same thing as saying that he proves it.
Some of Diamond's evidence is of the sort that can easily be proved. For example, when Diamond says that various animals like zebras have never been domesticated, that is a claim that is quite easily proved. Other aspects of Diamond's evidence are well explained but are not proved because they simply cannot be proved. For example, it is not possible to prove that Aboriginal Australians would ever have domesticated plants if they had had the chance. Diamond argues that they would have and he presents good points to support that argument. But that is not the same as proof. The very nature of this sort of argument (that a group of human beings would have acted differently in different circumstances) makes them impossible to ever prove.
So, Diamond explains all of his evidence, but not all of his explanations constitute proof.