These symptoms do cluster. Most people never ever experience halluzinations, but then they also experience delusions or other psychotic problems, relatively specific social problems, paranoia, etc.
In some sense this is a human-readable equivalent of logistic regression. Because schizophrenia isn't as well understood as some other diseases, you can only make "exact" models about meaningless abstractions, or create fuzzy models which allow meaningful treatment decisions.
The model is clinically useful, but the assumption (which the DSM does not itself advertise or support, which is made implicitly when its categories are used as the basis for research) that the diagnostic categories in the DSM represent commonality in origin is an impediment to research.
While many people have overstated the NIMH move away from DSM categories as a basis for research funding as something like an indictment of the DSM in its intended role or, even more hyperbolicly, a rejection of psychiatry as a field, it is an important move that recognize that the DSM categories' utility in their intended purpose does not imply that they represent real commonality.
Neuroscience tries to get a firmer grip on how the brain works, and what goes wrong when it doesn't. This research hardly touches the clinical practice as of yet, but ultimately diagnostics and treatment might improve largely.
Current models are fuzzy, but in the absence of better information they are the best we can do, and they are useful.
There are problems with having to match X of Y symptoms. Bob might be a close fit for 3 symptoms, and a weaker fit for 3 others, and not at all for the last 2. But, once Bob has the diagnosis, people interacting with Bob might not know what symptoms Bob matches and they might make assumptions - "People with your diagnosis do that because SYMPTOM".
It can be very frustrating.
There are two points to consider: (a) the principle underlying the hypothesis is sound vs. is not, and (b) the computational model of the hypothesis is deterministic vs. probabilistic. These two have to be considered separately when performing an evaluation/verification.