Earlier quoted context omitted.
Why should we want prediction markets to be fair? I want them to reveal facts about the world. They only need to be fair inasmuch as it serves that goal. I don't think it wouldn serve that goal to forbid insider trading? (Why do we forbid insider trading in the stock market? Not because it's unfair. Because it makes the market worse at doing what we want it to do, which is funding the most productive enterprises).
Given that inside information makes prediction markets more accurate, why do you believe it doesn't make stock markets more accurate? If, say, Enron insiders could've shorted their own stock, that would have improved accuracy and thereby diverted more funding to more productive enterprises. I guess there could be second-order effects when insiders can actually change the outcome, which is why athletes aren't allowed…
For example, if you happen to be a bartender or a waiter who accidentally overhears material non-public information, you're free to trade on that.