Why would you say “very?”
Famously, people have taken several tests a day - like Elon Musk - and had them read both positive and negative. He had no symptoms and does not believe those that read positive were true.
Define "true".
PCR can detect one gene from an RNA strand of one SARS CoV 2 virion. I believe that essentially all positive tests are accurate, in that, the tested person has at least one strand of SARS CoV 2 RNA at the site where the test was obtained.
What the presence of tiny quantities of SARS CoV 2 RNA MEANS is a whole other question. But the test, standing on its own specifications, is not "false".