Well, they sort of do.
Eating wheat causes intestinal permeability (look up "zonulin" if you're interested) and it is believed by many that intestinal permeability is the trigger to the body reacting to proteins it shouldn't. So if your gut is "leaky" you could be in a position to develop additional allergies and intolerances, not to mention autoimmune diseases and other crap. People with a sensitivity to gluten have the "gates" on their intestines opened longer than people without, but everyone has some leakiness due to wheat (according to a study published recently). It also seems other things can open those gates like pathogens and viruses and perhaps other foods.
Plus most folks with celiac disease are also lactose intolerant, due to the fact that the villi are damaged in their small intestines, so they can't produce the enzymes needed to handle lactose. But independent of lactose, I think a lot of folks are intolerant to other stuff in milk, like casein.
For me, I get gassy and constipated and bloated when I have dairy. It was hidden behind the IBS of the diarrhea sort I had when I was eating wheat. But it became more obvious after giving up gluten.
Enterolab.com does intolerance testing on a number of substances but you can, with good journaling skills and a disciplined elimination diet, probably figure it out for yourself. I have a feeling most of us just don't pay attention to the subtle clues our body gives us. Not that my clues were all that subtle... feeling like my intestines were going to crawl out of my body and strangle me.
Any time I have excess gas, bloating, diarrhea or constipation I know it is something I've eaten. I also found out I'm sensitive to pumpkin and sunflower seeds. They give me fierce diarrhea.