If I remember correctly that is from when the Bruce Willis character was telling a story about a fixed horse race that was thought to be a sure thing. But word got out because of how gamblers are -talkative- and then the race wasn't such a sure thing.

So my take would be that the line was referring either to folks who had inside information but couldn't keep their mouth shut or on the other hand, degenerate gamblers that were constantly pestering bookies or other people for information.