PCR stands for polymerase chain reaction. Its sensitivity is due to the fact that it can replicate a strand of RNA or DNA an infinite number of times. (That’s how they get DNA from tiny spots at crime scenes, for example.)
Our problem is that no test currently available can tell us whether a “positive” test of the virus is infectious or just a dead piece. That is leading to quarantines of perfectly healthy and probably not infectious people for months, and other possibly unnecessary precautions.
Contributing to this is we don’t know what is the minimally infectious dose of live virus. We can only get indirect evidence, which suggests somewhere between greater than one and less than that for measles. (Unless someone wants to be a guinea pig.)
They could do viral cultures. But those are time consuming and expensive.