Not ignorant at all... I believe the issue is that the statement ("95% confidence interval of 0.0 to 0.5") has just slightly different/counterintuitive meaning

Not ignorant at all... I believe the issue is that the statement ("95% confidence interval of 0.0 to 0.5") has just slightly different/counterintuitive meaning in this case. In general, you can always make the interval larger, but you want it to be smaller. With the understanding that the 95% is a lower bound, [0.0, 25%] is also a valid confidence interval. But, yes, you are entirely correct as to the practical meaning. 0% itself is impossible, but 0.0...1% could still happen.