There recently was a COVID* outbreak at an AI community space.

>20 people tested positive on nucleic tests, but none of the (only five) people that took PCR tests came back positive.

Thinking out loud about possibilities here:

1. The manufacturer of the test used a nucleic acid sequence that somehow cross-targets another common sequence we'd find in upper respiratory systems (with the most likely candidate here being a different, non-COVID, upper respiratory virus).  I think this is extremely unlikely mistake for a veteran test manufacturer to make, but this manufacturer seems to be new-ish (and mostly looking at health diagnostics, instead of disease surveillance).  I'm <5%
2. There was a manufacturing error with the batch of tests used.  I don't know if the group tried to re-test positive people with confirmatory tests from a different batch, but for now I'll assume no.  (These tests are not cheap so I wouldn't blame them)  This means that a manufacturing error could be correlated between all of these.  We have seen COVID tests recalled recently, and this manufacturer has had no recalls.  Fermi estimates from their FY2021 profit numbers show there are at least 2 million tests from last year alone.  I expect if there were a bunch of people testing positive it would be news, and a manufacturing failure narrowly constrained to our batch is unlikely.  I'm <5%
3. There was some sort of environmental issue with how the tests were stored or conducted.  Similar to the previous point, but this one is limited to the test boxes that were in the community space, so could be correlated with each other without being correlated with outside tests.  COVID tests in general are pretty sensitive to things like temperature and humidity, but also I expect these folks to have been mindful of this.  My guess is that if it were easy to make this mistake in an 'office building setting' -- it would be eventually newsworthy (lots of people are taking these tests in office settings).  Most of this is trusting that these people were not negligent on their tests.  I'm ~10% on this failure mode.
4. Some smaller fraction of people were positive, and somehow all of the positive tests had been contaminated by these people.  Maybe by the normal respiratory pathways!  (E.g. people breathed in virus particles, and then tested positive before they were really 'infected' -- essentially catching the virus in the act!)  These people would later go on to fight off the virus normally without becoming infected/infectious, due to diligent vaccination/etc.  I have no idea how likely the mechanism is, and I'm hesitant to put probability on biology explanations I make up myself.  I'm <10%
5. Unknown unknowns bucket.  One thing specifically contributing here is that (as far as a quick google goes) it seems like this test manufacturer hasn't released what kind of nucleic amplification reaction they're using.  So "bad/weird nucleic recipe" goes in here.  Secondly, I was wondering at the engineering quality of their test's internal mechanisms.  I couldn't find any teardown or reporting on this, so without that "internal mechanism failure" also goes in here.  Always hard to label this but it feels like ~50%
6. It was really COVID.  The thing to explain here is "why the PCR negatives".  I think it could be a combination of chance (at most a quarter of the positives got confirmatory PCRs) and time delay (it seems like the PCRs were a while after the positive rapid tests).  I'm also not certain that they were the same people -- maybe someone who didn't test positive got a PCR, too?  There's a lot of unknowns here, but I'm not that surprised when we find out the highly-infectious-disease has infected people.  I'm ~40%