I've understood that FizzBuzz is the lowest possible requirement for any programming job. It's a trivial programming exercise that doesn't require experience in algorithmic theory or mathematics. It's like going to the driving test and being asked to start the car: anyone who wouldn't know how to do that is likely highly incapable of passing the actual test.
Now, the astonishing issue, for me, is that there apparently are huge loads of people applying for programming positions who actually fail FizzBuzz. In effect, it's akin to applying for the position of a bus driver "coz I once travelled on a bus". I don't get that but apparently it does happen often enough to warrant FizzBuzz.