I don't have the Disney recipe, but I do cook greens (mostly mustard and turnip...we're not crazy about collards....but the recipe works the same for all of them).
Actually, there are 2 different ways that I cook them.
1) Fry several strips of bacon in a large pot. Remove the bacon and add your greens (make sure they are clean!). Stir the greens around in the bacon grease to get them coated fairly well. Add water just to cover and boil until tender making sure you continue to check the water level. You can put the bacon back in if you wish. Some people like it and some don't.
2) You can also use a ham hock instead of the bacon. The only difference is if the hocks are already smoked or cooked, then you basically put everything into the pot at once and let them all cook together.
It's pretty simple and I don't know if this is the way they are cooked at Disney or not, but I've never heard of cooking them any other way. We also eat them raw in salads and I like them that way too.