> You can tell because up to now, Uber could've been characterized as having an infinitely better fatality rate than the baseline. If a single data point takes you from infinitely better to 50x worse, the correct interpretation is: Not enough data.

No, you couldn't have characterized Uber has having "infinitely better" fatality rate than the baseline, because that would have resulted in a division-by-zero to calculate the standard error. Assuming a frequentist interpretation of probability, of course; the Bayesian form is more complicated but arrives at the same end result.

It's true that the variance is higher when the sample size is lower, but that doesn't change the underlying fact that Uber's fatality rate per mile driven is empirically staggeringly higher than the status quo. Assigning zero weight to our priors, that's the story the data tells.