Not directly, but in a very long round about way they do. Like if I have a mutation that is evolutionarily positive, the only way that helps me pass on my DNA is through the expression of the proteins, without them I could not do anything. The proteins, and their interactions with the environment, creates new information that indirectly results in a evolutionary pressure on the DNA and at a population level can change it.
How can DNA 'get' more information if not from the proteins interactions with its environment?
How can DNA 'get' more information if not from the proteins interactions with its environment?