There are many, many, in fact MOST, celiacs who can eat corn with no problem. I used to have bad reactions to corn myself, but now that my gut finally healed I can eat it again. Now don't get me wrong, I do not like the very idea of genetically modified foods, but I am absolutely sure that there is no wheat gluten in corn, any more than there is gluten in blueberries or almonds or any of the other many foods that made me sick before my gut healed. (I can eat them all now.)
And the reason celiacs have trouble with dairy is simply because the part of our bodies that produce the enzyme that digest dairy is the part of us that is damaged. It has nothing whatsoever to do with what the cows eat.
I'd love to find out who the maker of this movie is and what his/her credentials are.