Unfortunately that is not an interpretation that you would be justified in making - the test result doesn't tell you whether your immunity is winning.
Andrew, I think you're right in saying that in your Situation 3, those treating the patient may feel that a negative PCR and positive POCT make it more likely than not that the patient has had COVID-19 - if the symptoms had been very suggestive of COVID, such as loss of taste or smell. But they would be confident mainly because of those symptoms, not the POCT, I think.
Given the prevalence of other cold and flu symptoms that are not caused by COVID, however, and the incidence of false positives with POCT, I don't think treating clinicians would be confident to make the diagnosis on POCT alone, with nonspecific symptoms.
So in my view, the POCT adds a tiny piece to the clinical picture in this specific scenario, but not a lot. In Australia, this scenario - a COVID patient presenting more than 2 weeks after infection, with a suggestive history, no prior testing and now a negative PCR - would be very uncommon, because our contact tracing is so pro-active.
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