So, I obviously missed something "profound" when I read the term FizzBuzz for the first time and had no idea what it was talking about. I started digging in and was actually a little astounded (and saddened) by what I read.
I wanted to see if I could some up with something that would work. Obviously, I wasn't in an interview setting with someone breathing down my neck, but this is what I wrote in about 5 minutes. Basic testing shows that it seems to work. So, I don't know who this will help, but I am posting my contribution to FizzBuzz: