San Diego uses Run LT Run! Air Coryell went deep to John Jefferson ,Charlie Joiner and Kellen Winslow. Running was an after thought. Though he used Chuck Muncie more when he was there. Rivera would be the head man and could hire any OC he wanted (i.e. Norv Turner). A HC administrates the team and has to get along with the GM. Brian Billick in Baltimore was known as offensive guru in Minnesota has turned out to be a defense minded coach. Good coaches don't fix things that are not broke.
Yes, San Diego runs. They'd be neglectful not to. They still use the Air Coryell playbook, though, regardless of which specific plays they call.
You're kidding yourself if you think the head coach doesn't impose his philosophy upon the team. Mike Tomlin is going to install the Cover 2 defense in Pittsburgh. Nick Saban installed his hybrid defense here in Miami. Head coaches implement what they know. In Rivera's case, he would tinker with the workings of an already effective defense. But for the sake of argument, let's say Rivera wouldn't implement his defense. Why, then, should San Diego bother with a guy who's never been a head coach before, given that San Diego has all the pieces necessary to not only win a Super Bowl or two now, but to be a competitive team for many years to come?
And, lastly, why would Norv Turner leave his position as OC for the 49ers for the exact same position in San Diego?