DNA is not a neural network (that we know of), and I wasn’t meaning to imply it was. However, the actual neural networks (that is, meatspace neurons arranged in a live human brain) are tested simultaneously alongside the DNA and they succeed or fail to be propagated as a result of their fitness in the environment; the interaction between DNA, behavior, and acquired traits was once thought to be solely fiction, but it is actual science[1], though we don’t know much about how this works yet. The brain is as involved with your behavior and your DNA; I think that was the common thread in OP’s point.

[1] https://www.cell.com/fulltext/S0092-8674(11)01341-9