PCR testing that has been established for other pathogens has a much higher accuracy. So yes, in general PCR testing doesn't have that low of accuracy. PCR for COVID is a different story all together. Testing procedures were haphazardly thrown together by the CDC and/or other agencies with no updates to methodology since first being rolled out.
I've witnessed everything first hand. My wife is part of the process for those samples. She does sample accessioning and some pretest sample prep. My coworkers who run patient samples along with routine quality control samples continue to confirm the low accuracy rate. QA and management confirm these results.
My section is setting up a COVID wastewater lab. Since it's wastewater it falls under environmental. It uses basically the same PCR test; just slightly modified for wastewater instead of human samples. The lab is part of phase 2 of a pilot program being rolled out by the fed. gov't. We get to see phase 1 data and it's no better than what the clinical lab is producing. Our preliminary data is on par with that too. Our asst. lab director called it "the wild west of testing" meaning procedures and results are all over the place.
This is all internal. What lab leadership, State, and Federal agencies have released to the public is a completely different story. You can continue believing what you want, but I'll go with my first hand experience with it.