Having antibody doesn't mean you can't spread the virus. For example, antibody tests are often used to diagnose HIV, but testing positive for HIV antibody (i.e. you are infected) doesn't mean that life will be normal.
Also, while there would be concern about a positive but still shedding person coming into contact with one who hasn’t contracted it, there’d be no issue with them hanging out/working/etc with others who are positive.
Right now the only way to be whitelisted is having had a test done while being ill, but asymptomatic cases are unlikely to ever get tested.