I thought the point of the FizzBuzz was that the asker doesn't care about 'clever' (for some definition of clever) answers, but rather, "Can this person actually write something which solves the problem, no matter how brain dead a solution"

Only if you have no workaround or ability to implement modulo operations. If you were really a capable coder, but didn't know of %, you would just say, "I don't know of a library function for finding the remainder, so I'll just plug in remainder(x, 3) here." Then later, if such completeness is desired, implement that function.