[timr]

"And everything else in the CI. If we're treating this like a CI, then it's like saying a dice will land on 1, just because it's equally likely to land on 6. The actual P(1.5% | prevalence) is quite low at 3%."

You just said that you can't use a CI to estimate the likelihood of any point within the CI (you actually can, for well-behaved problems, but I digress) when I commented that 0% isn't a likely outcome within the interval.

Literally the same argument. If you want to argue that 1.5% is unlikely, then you have to accept that 0% is unlikely for the same reasons.