Isn't it effectively impossible to prove that a selection was truly random? Because if it correlated to something (so that we could verify that relationship), it's no longer random. Like if I made a random number generator, and it only ever outputs the number 4, I don't think there's any way to validate whether the RNG is broken or if this is just the exceptionally unlikely chance that the number 4 is chosen repeatedly.
Reminds me of this Dilbert comic[0]. You're correct that you can never prove that a sequence is not random. But looking at the probabilities could be enough to prove tampering beyond reasonable doubt. At the very least this would be enough to launch an investigation even if we were unwilling to draw conclusions based on probability alone.
