Too much of a good thing

Food poisoning doesn’t work that way. Either he over ate and is sick from over eating. Or he ate bad/contaminated/off food and he has food poisoning from that. Food poisoning doesn’t always occur straight after eating said food, it can be hours before it sets in.

... did he actually over eat? Or have food poisoning? Because you don’t get food poisoning the way you get alcohol poisoning.....

You can get both. Think Homer eating at a bad seafood restaurant. First he eats a truckload of shrimps and suspicious oysters, then his tummy aches a little because he overate, then since he ate more than his share of bacteria, he gets an extra-large food poisoning.

You don't get food poisoning by overeating.

Food poisoning is bad luck -- overeating is choosing to make a pig of yourself. They are two separate things.