That's accurate. Asymptomatic = not an issue to get an up chit (were never really down). FWIW, we had aircrew test positive on an antibody test, then negative on the nose swab. No further action required by medical or aircrew.I thought if you had an uncomplicated case and didn’t get hospitalized it was pretty simple now? At first, no. But I thought they put something out like that.
To the OP, depending on local policy, you may be required to report the results of any positive test out in town. That is the case here in Fallon. Probably not too consequential either way, but I'm not seeing the downside in letting your flight surgeon know so that it can be noted in your record.