question about gluten allergies

I have a weird question, and thought that one of you people who had researched food sensitivities might know about it. I know that people with gluten intolerance (celiac disease) have bad reactions when they eat high-gluten foods, and that some people with severe forms of the disease get bad reactions when they eat something with even a trace of gluten. Do other kinds of trace exposure cause problems, too? For instance, would it be dangerous for someone with the severe form of the disease to put a hand in a bowl of potato starch, without knowing if bowl might once have contained wheat flour? I know some catastrophic peanut allergies can require such intense vigilance and worry, but I don't know if someone is confusing the gluten problem with that kind of thing, or if gluten problems occasionally ARE that kind of thing.