That said, if the false positive rate were that high, the specificity of the test would be low.
"rigor"
Also, the error bars on these may be wider than is usual for an approved test, but they are just as likely to be understated as overstated.
Up to 20%, and I've seen numbers as low as 15% [1].
[1] https://www.webmd.com/cold-and-flu/cold-guide/common_cold_ca...
That said, if the false positive rate were that high, the specificity of the test would be low.