They do not have more fat when cooked. However, when you use the Search button for a food in FitDay, it somehow defaults to preparation with fat. You would be better off using the Browse Foods tab. Go to Vegetable, select the appropriate category, and keep going through the choices until you get to "fat not added in cooking." It's definitely more of a pain, but at least it's accurate.
And now that you don't have to be perfect, you can be good.