They are looking for antibodies to the spike protein on COVID-19. So if a person has those, then it's proof that they've been exposed to it.
Antibodies are unique for each virus, but there can be "cross-reactivity" where an antibody for a different virus also binds to COVID-19.
Yes, it is possible that there are people out there who have antibodies that bind to COVID-19, who have never been infected with it, but rather have an antibody that cross-reacts with COVID-19. But it would be a very rare occurrence.
So having COVID-19 antibodies isn't a perfect was to tell if a person has been exposed, but it's a very good way to do it since antibodies is highly correlated with exposure.
Antibodies are unique for each virus, but there can be "cross-reactivity" where an antibody for a different virus also binds to COVID-19.
Yes, it is possible that there are people out there who have antibodies that bind to COVID-19, who have never been infected with it, but rather have an antibody that cross-reacts with COVID-19. But it would be a very rare occurrence.
So having COVID-19 antibodies isn't a perfect was to tell if a person has been exposed, but it's a very good way to do it since antibodies is highly correlated with exposure.