I would expect that the low probability of reporting COVID given that you have a positive serology test is due to the fact that many COVID cases are asymptomatic. If I had no symptoms of COVID, but someone told me I tested positive for COVID one time, would I consider myself to have had COVID? I probably would, but I expect most people wouldn’t since “had COVID” is an experience centered on the experience of disease for most people (i.e. coughing and feeling unwell), not centered on the presence or absence of a virus in your body. The fact that half of the people who have a positive test result don’t think they have had COVID approximately matches my expectation about the rate of asymptomatic infection.
It actually lines up with the official terminology: The “D” in “COVID-19″ stands for disease. Not all infections cause disease.