There's another factor people often forget about - food poisoning from bacteria. Dairy products spoil quickly, especially if storage temperature is compromised or sanitation during preparation is poor. The symptoms can be severe: vomiting and diarrhea leading to dehydration, and in children this develops rapidly. I saw my neighbor take his son to the hospital after a milkshake from a roadside café - it turned out to be plain old E. coli.
But if we're talking about a truly fatal outcome, anaphylaxis is more likely. This isn't just an allergy in the ordinary sense - it's a lightning-fast bodily reaction that can develop in minutes. A person might not even know they have this sensitivity until they come face-to-face with it. Peanuts in the milkshake, traces of seafood (if prepared in the same place), even lactose with severe intolerance - any of this can trigger it.
Without details of the specific case, it's hard to say exactly what happened. But if it really was just a milkshake with no obvious killer ingredients, it's worth checking the milk quality too, checking for mold toxins or contamination. Unfortunately, it's not always obvious to the naked eye that something's wrong with a product.