New positives could be old positives. I know people who have tested positive for COVID 19 more than 6 weeks after recovering.
The one that also took an anti-body test also tested positive for anti-bodies. The virus can show up in tests when there is no chance of transmission.
Additionally, kids barely pass on the virus, even when infected, which is a lot less often than adults. So keeping schools shut – which will invariably mean day-camps – makes very little sense if there are no new real cases in a community. No matter what Trump haters say, he has science on his side when it comes to schools.
As an aside, NYC could have already met the states’s criteria to reopen phase one, if it made the planned hospital ship (IIRC in Red Hood) operational.