It doesn't. At least there is zero evidence that it does and there is a lot of evidence that it does not (i.e. simple hill climbing beats GA in every practical situation). I've mentioned this before on HN and reddit, but from time to time these kind of stories come up again. There is a weird fascination with genetic algorithms. Even though dozens of people have a career based on it, as far as I can tell the whole field of biologically inspired optimization algorithms is basically pseudoscience. Note optimization algorithms, so this does certainly not include e.g. neural networks, which work fantastically well.
That's a very insightful comment. The debate over whether recombination gives you anything "extra" continues in academia to this day. For example, papers on the controversy surrounding crossover in Genetic Programming (Luke and Spector in the 90s is a good starting point).