I don't understand the mentality of some that are worried because "he never coached running backs before".
All of these coaches aren't coaching in a vacuum, they are all around each other discussing all facets of football. The offensive coordinator talks to the running backs coach about his running game philosophy, the running backs coach discusses with the wide receivers coach about route running, and so on and so forth. My point is that position coaches interact with each other and are not in some bubble where they only focus on their position. In fact, it is beneficial for a coach to know as much about other positions as possible to make them a better coach for their position. A running back coach must know about receiving and blocking for instance since running backs also perform those tasks.
I'm sure Brown has been around Richardson and the rest of the staff and learned about coaching running backs as well other positions. He was the director of football operations for goodness sakes. Furthermore, I am sure that Brown, who I have no doubt already has some knowledge of the running back position, will take whatever steps necessary to learn what he needs to in order to be an effective running backs coach. I also trust Golden to hire good coaches and I'm sure he is obviously 100% comfortable with this hire.
I believe that the most important thing when it comes to coaching, specifically at the position level, is the ability to effectively communicate with your players. A coach can have all the technical knowledge in the world but if he cannot effectively communicate this knowledge to the players in a manner that they can grasp, then what good is all the knowledge? I want good teachers out of a position coach. It is much easier for the coach to learn the techniques of a position than it is for a coach to learn to be a great teacher/communicator.
I am more worried about Brown being a great teacher than I am about him not ever being a running backs coach because he can acquire all the technical knowledge he needs.