I think it depends on what you are talking about. A real allergy, where the dog reacts to the meat no matter how it is processed or cooked....or just a reaction to overly processed foods. Zane can have raw chicken just fine, but he can't have chicken meat, fat, or cartilage in poor-quality processed foods. In higher quality processed kibble, he doesn't react as strongly. So it isn't like he is allergic to the chicken itself. He reacts the same way to canned/processed green beans as opposed to raw/frozen green beans.
Some dogs can be allergic to the chicken itself though, and it seems to be to the meat only, like Jess and Allie said (although I personally wouldn't feed a food that had some parts of chicken and not others...I wouldn't be convinced it was completely free of an allergen, I guess).
And yah....they are all grains.