Comment by akoboldfrying

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.)