I had been programming for over ten years when I first ran into FizzBuzz, suffice to say I failed the exercise and wasn't offered the job. So I just moved onto the next interview and passed that one.

Sure, you can't prove that finding subcycles in a directed-graph is an NP-Hard problem on a whiteboard, or implement a linked-list or invert a binary tree by hand: But what you have is hard-earned common sense and a meaningful understanding of how software evolves over time. This is valuable to any company and many have identified that they are in desperate need of it.