PCR = chemical reaction with fluorescence
So what is the problem?
As with ANY chemical reaction, add more temperature, you will get more products. And the protocol is near the hot limit
Wait longer time, there will be more products. Again, number of cycles is near the limit for PCR device
Finally, primers. They should be specific enough but also robust enough. To distinguish between a virus and a dog is easy. Between similar viruses - guess what...
As a biologist I can call this bogus.
some 15 years ago, PCR was used as a rapid rest for HIV and the doctors were telling us: "kids, don't do anything stupid if you get HIV+, maybe it's false positive!"
RE: You can still test PCR-positive after being fully-'vaccinated'