A good interview exercise (not necessarily vouching for fizzbuzz here) allows depth of discussion past the initial answer. It is in this discussion stage where I spend the majority of my time with a good candidate.
In such a discussion we might talk about whether it makes sense to make the /15 case "fall out" naturally. Using your example, there's an implicit assumption that the requirements would change to {4: fizz, 5: buzz, 20: fizzbuzz}, but in real life I've found things have the annoying tendency to change to, e.g. {4: fizz, 5: buzz, 15: fizzbuzz}.
In such a discussion we might talk about whether it makes sense to make the /15 case "fall out" naturally. Using your example, there's an implicit assumption that the requirements would change to {4: fizz, 5: buzz, 20: fizzbuzz}, but in real life I've found things have the annoying tendency to change to, e.g. {4: fizz, 5: buzz, 15: fizzbuzz}.