What's the attitude of sports' governing bodies towards gambling?

I’m curious about how various sports’ governing bodies feel about gambling in that sport. I’m obviously not talking about gambling by participants in the sport, which I’m sure is usually verboten. But how much are the interests of the gambling public taken into account? For thoroughbred racing, it’s pretty obvious, but how about the NFL or FIFA or the like? Is their posture one of studied neutrality, hostility, veiled encouragement? One specific instance comes to mind, and that’s the NFL rule on injury reporting. Is the purpose there to seek parity on the playing field, or to keep oddsmaking more honest?

All* sporting-governing bodies I am familiar with condemn any sort of gambling for fear it would taint the game and reduce it to the level of Pro Wrestling or Boxing. The amounts of cash involved in illegal betting is already so vast that there is a real danger that a player (like Pete Rose) might be tempted to fix a game just to cover gambling debts on games outside his own sport.

That would be Real Bad.
*Save only Horse Racing and Jai Lai.