And no matter how small a probability someone assigns to "the randomness is unfair 'cause the experimenter is a dick", picking red will yield epsilon more expected money than picking green. You need a probability of exactly zero for the choices to be equivalent.

Of course, in an abstract thought experiment as described, a probability of zero is indeed implied, but people don't pay attention to instructions, as anybody doing tech support will tell you - they invent stuff that was never said, and ignore other bits (I'm guilty of that myself - we all are, I think).