I thought they were more common on the fast tests that MLB is probably using? The tweet from Dougherty indicates he has more than one test yesterday so they must be quick turnaround.
A family member tested positive. Ironically it was a false positive. And the cause was a transcription error - preliminarily it was reported by a human as positive, then subsequently corrected. But in the interim, I did a bit of research and concluded that most false positives are that sort of error. So, we can hope that it's a transcription error in Soto's case, but it doesn't happen often.
A false negative occurs because the virus isn't found in the sample. Doesn't mean it's not there. For example (not too be too graphic) I had a prostate biopsy about eight years ago. They took 12 core samples and found cancer in one. Could have just as easily missed that core, I would have come out negative, but I'd still have cancer, in fact I've had two biopsies since, both completely negative, but the cancer is undoubtedly still there (no worry, I'm assured I'll die of something else before it becomes a problem).