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.