I agree with everything you've said here. The question you begin with is a good one. It could have indeed happened naturally. This is the $64,000 question. Has it been demonstrated that random mutations and natural selection are capable of generating specified complexity? If it has, I am unaware of it. Dembski has said repeatedly that if it can be shown that these two mechanisms, or any set of natural mechanisms can generate specified complexity, his theory will be refuted completely. PMFJI, but three words: vertebrate blood clotting.
The genes involved in blood clotting have been shown to be closely related to a smaller number of genes in the distant ancestor species (information increase), and the functional steps from the original pancreatic enzyme to the current refined, multistep self-catalyzing process (specified complexity) are plausible (not IC). And the theory has survived an attempt at falsification from Behe intact.