I don't think Miami runs this exact offense...before Tua went down (granted it was only 1 game), I want to say that they threw the ball more. <- maybe it is....but it doesn't feel like it.
Both offenses are from the Shanhan/Kubiak tree. Certainly they call plays a bit different, there are some different wrinkles, and Miami probably throws more than we do, but it's still the same scheme. My only point is that the scheme can be adjusted to the personnel you have so you don't have to exactly match the personnel they have in San Francisco to effectively run this scheme. Miami is an example of a different way to do it. And I would argue that a good OC might have a style they want to play, but they adjust that to the players they have.
In the case of the Saints, it's probably smart to go run heavy since our very questionable OL is much better at run blocking than they are at pass blocking and if you show enough run it means you can throw the ball with play action to help protect an OL that is bad in pass protection.