If anything, the test used skewed towards higher false negatives than false positives.
That doesn’t matter for the problem we’re addressing this thread. What matters for this thread is the relative size of false-positives to true-positives; false-negatives have almost no consequence for the arithmetic we’re conducting in the experiment in question.
So the argument is really, the range is not calculated correctly, or the math used is wrong.
No—neither of those statements is on-point.
Please reread
If you have a test with a >1% false positive rate, then you cannot know if the true rate in your population is 0.01%, 0.1% or 1%
You are trying to measure something with an instrument that lacks resolution. It's like measuring the speed of light with a pocket watch