One of the Travel Channel behind the scenes shows talked about them. They use a specific breed of bird and inject a brine to flavor and retain moisture when cooking.
Ah ha! Found it:
Another Signature finger-food snack at WDW is their Giant Turkey Legs.
In fact, they sell 1.5 Million Turkey legs a year. That's a lot of legless turkeys!
Alot of people think they are fake, and perhaps Emu or Ostritch legs, because they are so big. But the turkeys are actually raised in the upper mid-west and weight 40-50 lbs. So the legs you buy are a whopping 1.5 lbs.
The secret to the unique flavor is the salt water curer injected into the leg muscle tissue and then each leg is slow cooked for 6 hours.
I've never had them just because I only eat white meat, but I admit they smell really yummy everytime I'm there. I'd be curious to try a bite, but I don't want to buy a whole one knowing I won't eat it.
-m