However even if an individual did have cross-reactive antibodies they likely wouldn’t be good enough to prevent the virus as, due to the novel nature of the virus, they wouldn’t recognize them particularity well. Therefore at best you’d probably get slightly milder symptoms. In a nutshell, the antibody tests have a yet unknown specificity and some people assume that they are significant false positives by the response to common cold coronavirus variations. The methodology of the study and its conclusion has been criticized. Note that this is not peer-reviewed. The core of the critique is that the test used did not test for SARS-CoV-2 immunity.
Isn’t it too premature to say they are immune? What about reports that some people are getting sick again after recovering? The virus could be lying dormant inside them until it flares up again. Those with detectable levels of antibodies are likely immune, their body has kicked out the virus and created those antibodies in response. However, there’s no knowing how long those antibodies will stick around to protect you. We also don’t know what level of antibodies is necessary to fully protect you. We do see some signs that people who had “mild corona” make fewer antibodies, which could be worrisome.