I don't really see this as being any less trivial than proving inverses are unique. Both require writing down the statements, and a couple applications of the group axioms.
I like my phrasing a little bit more because it at least requires knowledge of the definition of a group hom. Fizzbuzz also requires little more than an understanding of for loops and if statements, so I'd say they're kind of similar.
On the other hand, I know a couple extremely good analysts who would stare blankly at you until you reminded them of the definition of a homomorphism =)
To be clear, however: I think these are pretty good analogues of FizzBuzz.