The impact of coincidence on psychiatric diagnosis
Your question is a bit complicated because it has two possible underlying assumptions or questions.
Firstly, it involves the one of premonitions. In your final statement you are implying that there is no scientific proof to suggest that premonitions can exist. On the other hand, is there scientific evidence that premonitions cannot exist? It is a grey area, open to speculation and interpretation of personal testimonies.
Also, you are suggesting that the psychiatrists would definitely be regarding the existence of premonitions as psychosis. I would say that many psychiatrists are inclined to diagnose people who explain unusual experiences as psychosis, but that is not to say that all have fixed views about matters of the unknown.
I would say that I have engaged with psychiatrists, and other mental health professions, in work and situations, on the subject of premonitions and other unusual topics and some of them are have very unique points of view.
I would say that psychiatrists would differ in how to respond to your scenario. It may also depend how the patient explained the story. I certainly feel it would be mistaken if the person was diagnosed on the basis of the scenario, unless there were other sources of concern. Of course, I am not a psychiatrist but have worked in mental health care and been involved in the psychiatric assessment process. I think that it would be unfortunate if your person acquired a diagnosis and ended up on antipsychotic medication. Perhaps a bit of counselling support to discuss the whole coincidence would be the best start and some follow up to see if there were any further indications of psychosis beyond this would provide a fuller picture, as ongoing assessment.