It has been said that there is some likelihood that exposure to a previous Coronavirus made some people partially resistant to Covid-19. Would that mean that there is a chance that some people test positive for Covid-19 antibodies due to a different strain of Coronavirus?
It's also possible that some people are fighting off COVID via a T-Cell response while not developing significant immunoglobulins or that immunoglobulin levels fade quickly while T-Cells don't. Those people can also test negative for immunoglobulin antibodies despite fighting off the disease.
So it's actually more likely that these tests are significantly under counting exposed people in total. But these tests aren't perfect and for any specific person, they could give you a false positive or a false negative result.