I'm not sure thats true. Those positives often seroconvert so they were infected. Were just catching them on the long RNA fragment tail.
Between March 26 and April 10, 2020, we measured SARS-CoV-2 antibody titres in 1343 people. Of the 624 participants with confirmed SARS-CoV-2 infection who had serologies done after 4 weeks, all but three seroconverted to the SARS-CoV-2 spike
https://www.thelancet.com/journals/lanmic/article/PIIS2666-5247(20)30120-8/fulltext