If someone thinks he's schizophrenic when he's not, is he diagnosed with hypochondria instead?

Many possibilities: Not all psychotic illness is schizophrenia -- there are still other possibilities that might apply in his case. People with hypochondria rarely think they have a psychiatric illness, but it can happen. The most reasonable approach (if he's willing) would be for him to see a psychiatrist for an evaluation. This can help clarify things, and provide any needed assistance.