Understand, most real world programming jobs don't need in-depth knowledge of algorithms and data structures. Most real world programming jobs are implementing the algorithms devised by someone else, using data structures that are "obviously" the right structure for the job. When companies are asking these sorts of questions they usually have a somewhat inflated view of their own importance. Either that, or those interviewing have no real idea about the work done by their programmers.
The very best interviewers, when using these questions, don't worry too much about the detail of the solution, but in the discussion of the pros, cons, benefits, drawbacks, and possible development of the code in context. Even with FizzBuzz there is much to be explored once a coder has written it.