Whenever I read about "independence", it raises a red flag in my mind. If a paper contains a probabilistic analysis, bugs or even errors can often be hidden behind the word "independent". I am slow in believing independence, and especially conditional independence. That's where I have seen many bugs come up in proofs by me and by others. I am now skeptical of any unproved claims of independence.
Is the pro-Colbert super-PAC “Americans for a Better Tomorrow, Tomorrow” independent of Colbert? As it exists in real life, we are assuming, barring evidence to the contrary, that it is not coordinated. But if it came up in a science paper, we would ask to see a proof.