Do you have links to these widely reported false negative results?There are the widely reported false negatives. It's impossible to examine the the idea of false positives.
That's not a facetious question. I suspect what you are thinking is a false negative is the lack of an appropriate test, which is not a false negative, but an example of the cheaters being a step ahead of the testing. The development of validated testing regimes takes time and the labs are always playing catchup on the cheats.
The concept of a false positive in drug screening at the laboratory does not make much sense. If a drug is found in both the A and B, it is because it is present.