This has been hypothesized for some time, as it is a phenomenon seen in other respiratory viruses (indeed in other viruses in general) where your test is detecting a fragment of virus. These fragments persist after clinical recovery, and, combined with imperfect sensitivity/specificity of your test, can show a pattern of "re-infection": positive test during illness, negative test during/after recovery, then positive test again later.
The gold standard (sort of) for whether the actual virus is there is isolation and "culture" of virus from a swab using, say, a petri dish. But unlike (most) bacterial pathogens, this process is laborious, requires actual relevant cells (many bacteria just grow in goop like Agar) and is slow. (Alternatively you could just try to infect someone else! And if that second person can subsequently infect someone else, then you've shown the virus was there in the first person. And the second person. Sorry, second person.)
Empirically in hospitals we've been seeing a couple of patients retest "positive" but haven't seen any get sick or re-hospitalized, so that's also reassuring.
They found that, for all patients in the small study (N=16), none tested positive for infectious virus after day 8 post-onset, despite testing positive for the virus in RNA over 2 weeks after illness onset. This, to me, is encouraging.
The gold standard (sort of) for whether the actual virus is there is isolation and "culture" of virus from a swab using, say, a petri dish. But unlike (most) bacterial pathogens, this process is laborious, requires actual relevant cells (many bacteria just grow in goop like Agar) and is slow. (Alternatively you could just try to infect someone else! And if that second person can subsequently infect someone else, then you've shown the virus was there in the first person. And the second person. Sorry, second person.)
Empirically in hospitals we've been seeing a couple of patients retest "positive" but haven't seen any get sick or re-hospitalized, so that's also reassuring.