If this is rare enough, it could fall into the false positive rate of the COVID test they've previously done (i.e. while the test said they had COVID, they didn't)
You could be PCR tested positive, while experiencing a cold or flu (which you would now understandably think were Covid symptoms), but would not have immunity for a future, larger infection from Covid.
Though statistically unlikely, it's bound to happen sometimes.
Remember that immunisation makes antibodies but only provides something like 50-95% protection (depending on the vaccine) - it's not surprising that actually catching it does the same thing