As an anecdote, I asked my wife, who's not a developer, she is an executive at a large beverage company, to solve FizzBuzz and to explain to me how she would do it and she did it successfully. She didn't use the word "for" or "while", but she explained that she figured there must be something that allows you to iterate over the same algorithm several times (paraphrasing).
Personally, I think FizzBuzz are useless unless you use them as part of a submission form before candidates send in their resumes, sort of like a slightly harder captcha. There is no place for a FizzBuzz once the company is already engaging with the company, if they are not able to solve it they will be earlier signs that they lack common sense and criteria.