If it's the nasal swab-PCR test that most civilians are getting, then the claim of "asymptomatic" must be accompanied by a "yet". We can't really conclude anything for at least two weeks after the positive result -- after seeing whether those people ever develop symptoms.

If it's blood-antibody testing, then we can give the statement a little more weight, because a positive result would mean the infection is in a later stage or even past. I have no idea whether the Navy is using these tests.

This is in the bay area, where people were very quick to self-quarantine. Most people have been working from home since early March. They were asking people to break their self-quarantine to get tested without having any symptoms?