Yeah, at face value the two diagnoses are positively correlated. This is simply true. And traits of these two only become negatively correlated if you remove the shared social difficulties, which includes a lot of the negative symptoms. Unfortunately everything is positively correlated in psychiatry. If you want to explore this deeper I recommend the "p factor" (general psychopathology factor), which is a serious, multi-year attempt at identifying something like the "first eigenvector of psychiatry", a loading common to all psychopathology, including substance use, affective disorders, psychotic disorders, conduct/personality disorders, ... The idea is that if you only know that someone has whatever goes into this vector then you know that person is quite likely to develop some disorder, but you don't know which one.

I would only add that ASDs do not have "real" negative symptoms of schizophrenia, but what they do have can look a bit similar. The research on anti-correlation was using questionnaires and binned the social questions taking that into account.