”Without further knowledge, the calculator cannot know that a negative number is impossible (in other words, you can't have -5 civilizations, for example).”

Not true. If there are no negative terms, the equation cannot have negative values.

The calculator cannot know whether there are no negative terms. For example, if people's net worth is distributed 0.2–400, there's likely a significant chunk of people who are, on the whole, in debt. These will be represented as a negative term, even though their distribution was characterised by positive numbers.

The range notation indicates 95% confidence intervals, not the minima and maxima. If the lower bounds are close enough to zero (and the interval is large enough), then there may some residual probability mass associated with negative values of the variable.