Basically, Diamond can make such generalizations because that is what all social scientists do. Social scientists have to do things like categorizing people or societies so that they can have some way of thinking about them. For example, we talk about both the United States and Great Britain as democracies even though they have very different political systems.
Diamond makes these generalizations because he has to be able to talk about the different stages that societies go through. It is clear that there are differences between societies and it is important for Diamond's thesis to talk about what attributes each sort of society has. In order to make any sense of the range of possible societies, it is necessary to make broad categories.
As Diamond says, categorizations are "doomed to imperfection" but they are better than nothing. That is why Diamond can make such broad statements.