Admittedly, I only read the headline. But doesn't that simply mean that by the time some tests have taken place, they're no longer infectious but in reality have already spread it anyway? It doesn't mean "oh your positive, but can't spread it" more like it's "oh, actually you've got it but you've spread it already" so to speak.
Not doubt, but if they are picking it up after they have been infectious do they know when they were.
It seems quite a big issue if we are basing everything on tests