No, the factors causing the false positives are usually correlated. The most common cause is mutations causing unrelated proteins to mimic an epitope (binding site) of the biomarker protein. Another cause is analytical interference where some other molecule absorbs the wavelength used to measure the assay.
Running the test using multiple different labs helps eliminate contamination and handling errors but most false positives are due to genetics and long term environmental factors.
But if you got one test saying "Detected a fragment of pancreatic cancer DNA" two days later another saying "Didn't see any cancerous DNA fragments" what would the actual effect on the doctor or patient be? Who'll take the risk and say "the first was a false positive"?
Also, these tests are a grand a pop if I'm reading it directly (which I may not be)
I think it can always be blind process. Only notify when good probability. Plus it can be funnel to other non invasive (possibly) tests.
They do cost a lot but that may change with time and scale.