Jacob Gershman of Slate looks into misleading fiber claims found on cereal and yogurt packages. He explains that there are two kinds of fibers: dietary (found naturally occurring in plants) and functional. The added fiber found in most food products are functional, like polydextrose and inulin. Since FDA-approved food labels don't distinguish between dietary and functional fiber, the polydextrose found in a box of Cocoa Pebbles may be labeled as a dietary fiber even though it's not the same thing:
...Nobody knows if these fiber additives possess the same health benefits as natural fiber found in whole grains, fruits, and vegetables. [...] Even when it comes to the natural, wholesome stuff, like oats and kidney beans, nutritionists don't know for sure whether the health benefits derive from the fiber itself or from the collective impact of high-fiber foods.
Gershman says that food manufacturers are getting "more clever at manipulating ingredients of snacks and other treats so that the stats mimic the nutritional data of fruits and vegetables," which goes to show where you should be getting your fiber from: fruits and vegetables.