Food poisoning is rare. If it were food poisoning, there would be whole bunches of people complaining about it based on a specific restaurant. Think about how you read about an issue with food poisoning at a local restaurant. The media and Board of Health is all over that, yet when was the last time we heard this about a Disney venue?
Stomach virus on the other hand (especially the noro types) are quite common in crowded places. Sorry to be gross, but this virus gets passed on when someone who is sick didn't wash well after the bathroom, touched something you later touched, and then you touched your mouth.
Disney is more crowded than a cruise ship, day care, nursing home, etc., and think how often we hear about one of those places having noro going around. Also, the amount of children, who unfortunately don't always have the best hand washing skills, is huge compared to those other places. Factor in how many handrails, seats, seatbelt fasteners, etc. you touch at Disney and you can see how these complaints are not food bourne illnesses.