I appreciate the usefulness of the bootstrap in obtaining uncertainty estimates, but one thing that's always bothered me about it is that the distribution corresponding to those estimates is the distribution defined by the sample. In general, it seems like a bad idea to believe that our sample frequencies look exactly like the underlying distribution, so why is it sound/acceptable to derive uncertainty estimates based on a distribution where the sample frequencies define the underlying distribution?

On the other hand, this may be no worse (possibly better) than other distributional assumptions we typically make, but I'd still like to understand the justification a bit better.