The false positive test was for antigens. Tests like that are known to be less accurate: https://www.sciencemag.org/news/2020/05/coronavirus-antigen-...

The two negatives were PCR tests. Those are different from antigen tests. The blog post you've linked says there is a problem with false positives with PCR tests, but that doesn't seem to be relevant here, given that both of those results are negative.