Fruits are much higher in sugars than leaves which an insectivore (even one with the ability to eat leafy greens) is not used to digesting. In the wild, eating berries is generally associated with an attempt to increase hydration in the dry season, not necessarily an attempt to gain any nutrition. Since it most likely is only a seasonal, uncommon resource usage, these animals are still not designed to handle large quantities of fruit. As a result, I don't think the practice of including fruit in the diet is a good idea. Similarly, you wouldn't feed a dog large quantities of fruit for similar reasons. Whether or not it definitely causes problems is unknown but logic would indicate that this practice is not necessarily beneficial.
Chris