The issue is that many samples do not contain virus. As far as I know, that has not been quantified outside of China. (2)
1. https://www.fda.gov/media/136151/download
2. https://www.mdmag.com/medical-news/comparing-rt-pcr-and-ches...
The PCR test itself has near 100% sensitivity and specificity when done correctly.
Poor swabbing or contamination can result in false negatives or positives.
Manual PCR testing is known to be quite prone to human errors hence why the all in one cassette kits are quite popular.