Actually the PCR can only work with viral debris. That is, parts of the virus that are left in the bloodstream after the cells destroy it.
This means you can never know if someone has the virus, only that they had it and overcame it.
There's also the issue of how many times they amplify it. If you amplify it more than 20 times, you could be picking up debris from a single virus that was never a risk of infection or contagion.