Because these markets aren't all that efficient yet (possibly because other potential market participants are scared off by insider trading charges). You don't have multiple people that all have insider information betting against each other, you have one person with insider information that cleans out everybody else. If this repeats enough, all the people without insider information will get cleaned out and exit the market, all the other people with insider information will enter the market for profit, and prices should converge to true likelihood.

And yes, the whole purpose of prediction markets is to turn insider info into public info.