I've read the Coding Horror article you mention, and my opinion is that Jeff is right... but when is the last time he got interviewed?
When you are interviewed, you are usually in high stress, and you often have to answer to theorical questions (no intellisence, no google, no resharper, ... only your memory troubled by stress). That's the same in tests. Stress doesn't help you.
I've noticed that the only way to know if someone is suitable for a position is to work with him for a while... Just take the last 10 persons you hired out of 100 (maybe more), how much was a really good hire???
An employer should hire a problem solver, not a code monkey that know about modulos.
You can't test "for a while all applicants", so interviewing them is required. That's why I focus my questions on that (problem solving) and do past reference check.
My opinion is that the FizzBuzz is dangerous for the company that is looking for developers to substain its growth.