They are worried true positives of IgG would lead people to expose themselves, since IgG is only one part of the immune system, and IgG to the very specific target in the test is not a description of the entire repertoire of anti-COVID antibodies present, and therefore the antibody test is really only a test of prior exposure, not a validation of the immune system of the recipient.
Moreover, people can still act as fomites (passive carriers) even if not infected.