Consider two probability distributions $D$ and $U$, over $n$-bit strings, where $U$ is the uniform distribution. We are not given an explicit description of $D$: we are only given black-box access, ie, we are only given a sampling device that can sample from $D$. Consider a sample $z in {0, 1}^{n}$, taken from either $D$ or $U$. We want to know which one is the case: we consider polynomial-time algorithms that use the sampling device.

Intuitively, it seems obvious that the best polynomial-time algorithm that distinguishes which distribution the sample $z$ came from must have gotten that very $z$ as a sample at least once when running the sampling device. How do I mathematically formalize this statement?