My hospital error rate is 2 percent so 98 percent accuracy of the test itself. That stated, it also depends on if the nurse does the test correctly. Gotta check both nostrils and go all the way back to the sinuses for a full 15 seconds each side. That assumes the virus is in the sinuses and in many it is; however, we have also taken intubated patients and done a bronchial wash by going down into the lower respiratory tract and pulled that out and sent it down. The sample is run through PCR aka polymerase chain reaction where they multiply the sample into billions of DNA strands and then tested so even if you have a small micro-piece-of-snot, we can pick it up because it will be multiplied. I've had it done once, not very pleasant but I told the nurse to go for it because if it was there, I want to know so gotta just push the discomfort out through the feet like a boxer does when they get hit in the face.
But there are numerous types of tests out there currently. We were sort of left high and dry by this administration so hospitals came up with their own testing and some companies were able to streamline it independently and package and sell it to hospitals. (On my soap box a little bit). Now, if someone gets admitted to the hospital, they are going to get tested. If they are showing classic COVID symptoms like screwed up chest x ray, elevated d dimer, jacked up liver enzymes, normal WBCs showing a systemic infection, I can usually get results back in 3 hours but if they are just a normal admit for GI bleed or something like that and I'll likely get that back in 12 to 24 hours because we are just being safe and not exposing staff blah blah blah but it's like Oprah at XMAS, everyone gets one.
Long answer to short questions but just wanted to be thorough. Outside the hospital, there is a significant lag because it has to get sent to outside laboratory.
To clarify: I've never seen a negative later report as positive.