Are you saying that while test results are positive, they’re not COVID19 specific, therefore not indicative of true results?
Yes serous question
Yes, that may very well be the case. The study authors included no controls of people who have had the common cold (preferably confirmed to be caused by a coronavirus), which are needed to show that positive results are, indeed, Covid-19. Given the cross-reactivity that most antibodies exhibit and the similarity of all coronaviruses, I am not at all convinced that they were specifically measuring Covid-19 antibodies.
Several years ago, I took a cat to an emergency hospital and the attending vet ordered an FIP test for the cat. FIP is a coronavirus that causes fatal disease in cats. The test came back positive, but based on the clinical symptoms, the vet said that she was "not impressed" and did not diagnose the cat with FIP. (The cat had a severe immune disease that caused massive blood clotting and low blood cell counts. Miraculously, she recovered and lived another 9 years.) The FIP test was, in fact, approved by the FDA for clinical use, meaning that it met certain standards of specificity and sensitivity. Given that the FDA approved test can give false positives, I am not at all convinced that a research grade kit that has not been validated is accurate.