Earlier quoted context omitted.
Natural data is easily identifiable.
Only if you count all natural looking data of which there is way more than you could possibly imagine. It is of course likely that humanity hasn't yet created more than 2^100 (~10^30) files, so in theory given a registry of all files in existence you might be able to identify it by its hash. However while this is simple it's definitely not easy.
It's an issue of probability and bins. While natural data is infinite, there is vastly more unnatural data. At some point you have enough metadata (e.g. natural vs. random) to know that the original data came from Earth to pick out the right needle from the needle stack.
Unless the data is from a completely alien source, we are close enough to that source for our heuristics to be of a manageable size.