The Stanford study in Santa Clara that used Premier Biotech appears to be very misleading. Given the confidence intervals on the specificity all 50 positive cases out of the 3330 tested could just be false positives.
Especially considering the test used here was also, Premier Biotech's. Their manual [1] states, that other coronavirus strains can lead to false positives in the test:
>Positive results may be due to past or present infection with non-SARS-CoV-2 coronavirus strains, such as coronavirus HKU1, NL63, OC43, or 229E
See Gelman's article on the topic.
https://statmodeling.stat.columbia.edu/2020/04/19/fatal-flaw...
I am similarly skeptical of the findings here.