Donald E. Simanek has a nice Fibonacci webpage where he discusses some of the foolish claims that others make. You may have seen tons of those Fibonacci meme type images on the interwebz recently. David says:
Of course much of this is patently nonsense. Mathematics doesn’t “explain” anything in nature, but mathematical models are very powerful for describing patterns and laws found in nature. I think it’s safe to say that the Fibonacci sequence, golden mean, and golden rectangle have never, not even once, directly led to the discovery of a fundamental law of nature. When we see a neat numeric or geometric pattern in nature, we realize we must dig deeper to find the underlying reason why these patterns arise.