That is too strong a conclusion. People with nut allergies already have procedures for knowing if nuts are in food, for example, asking the restaurant or preparing food their self.
Without knowing if his app was accurate, we cannot say whether building or not building the app was the right decision.
Humans aren't any better at determining if a kiss has invisible almonds. An AI could solve that (better than a human could!) by knowing memorizing ingredient lists form public databases and tagging foods that have nutty variants, often times that people wouldn't know about.
I think it's fair to say humans are better at reasoning about uncertainty and risk. If the food isn't in the database, or we aren't sure if it's a match, what does the algorithm say?
ML algorithms work on statistical performance against loss functions or error rates. They aren't (yet) good at understanding the difference between a mistake that causes a missed dessert and a mistake that might kill you. Maybe they can guess correctly a higher percent of the time if shown flashcards, but that's small consolation from the hospital bed. They also aren't that good at the limits of their own knowledge, i.e. saying "I don't know".
Without knowing if his app was accurate, we cannot say whether building or not building the app was the right decision.