alt Hacker NewsSure, but we shouldn't stretch the analogy too far. Die rolls are discrete events, while miles driven are continuous. We expect the number of sixes we get to follow a binomial distribution, while we expect the number of accidents to follow a Poisson distribution. Either way, trying to guess the mean value of the distribution after a single incident of the event will never give you a statistically meaningful lower bound, only an upper bound.
The Poisson distribution is well approximated by the binomial distribution when n is high and p is low, which is exactly the case here. Despite the high variance in the sample mean, we can still make high-confidence statements about what range of incident rates are likely -- basically, dramatically higher rates are extremely unlikely. (Not sure, but I think it will turn out that confidence in statements about the true incident rate being lower than observed will be much lower.)