Have zero idea how they get a bad positive? It seems clear cut, a yes or a no. Not saying I'm a virologist or microbiologist but testing something for a yes or no shouldn't have so much error in it. I'm mind boggled on this.
People don't understand all the factors that go into a test.
Which type of swab was used? There's one that looks like a pipe cleaner (first one approved) and a Q-Tip looking one. The Q-Tip one is less comfortable if used properly (inserted all the way to the nasopharynx, the back of the nasal cavity)
Was the swab properly inserted all the way to the back? (from experience and anecdotal evidence, many administrators of the test accede to the discomfort of patients and don't push the swab all the way to the back, especially the larger, Q-Tip looking swabs as opposed to the pipe cleaner looking swabs).
Which type of test was used? Typically, rapid tests are meant to grab obvious positives. They are an effective screening tool, but should never be the ONLY tool used in any screening protocol. I would wager it was a rapid test false positive followed by two more comprehensive tests which both yielded negatives. As in almost all things, accuracy is sacrificed for rapidity
Lastly and especially for coronavirus testing of any kind (common cold, flu, SARS or COVID), the accuracy tends to be low (sub 80%) because initial testing could pick up antibodies relating to any of them, yielding false positives. They found this early in folks who'd had SARS. For diseases with low to no mutations, tests can and do tend to be very accurate. We know what to look for and design tests to be very specific. For diseases that can and do mutate, there a LOT of factors involved that can lead to both false positives and false negatives.
And that little tidbit barely scratches the surface.
Put it this way... there's not a single particle, molecule, cell, cell byproduct or process that we're testing for which is definitive, so it's not a binary "yes/no". Not in the way that a smallpox test would be, for example.
One day we may get to that point, but alas, we're pretty far from that.
We'll have widespread use of robotaxis and unmanned trucks on the highways in less than 10 years, but it'll be a LOT longer before medical science refines its understanding of the human body to have definitive tests like what you're referencing.
People are kinda complicated, it seems.