I think the counter to that is the belief amongst the coaching profession that 'success' and 'how good a coach is' is highly situational. We have seen it before where a coach or coordinator struggles in one setting but gets an opportunity elsewhere and looks like a different person. It does happen. How often, I really don't know. I was thinking about this when I heard the Turner news, but the reason why fans and the coaching fraternity view these things in almost opposite terms is due to our 'relationships'. For a fan, the relationship with a coach is enmeshed with success and winning. Without the latter, we quickly become hostile, even angry. Look at Jack Del Rio. A slow start by his defense and fans demonize him and want him run out of town on a rail. Get the defense going, the strength of the team in fact, and all of sudden Jack Del Rio is good to go in the eyes of fans. It's just how we are.
In the coaching community, you aren't wrong about the constant recycling. But I think its based on relationships as well - in the case of coaches they are long-time personal ones. The 'coaching tree' is a real thing. These guys come up through the ranks, they understand how fickle fans, GMs, and owners can be, how hard it is to consistently win in the NFL in an age of relative parity and the 'win now' imperative. They empathize with each other, identify with each other, and they know each other. Scott Turner may be one hell of a guy. We don't really know him. And I think coaches believe a stint in one location, even a long one, doesn't define anyone one way or the other. Maybe the truth and 'fair' is somewhere between the fan's 'fire the bum' and 'he's a good coach, it wasn't his fault in Washington'?
And look... while I get what you are saying the fact is that Turner got fired and now has to accept a demotion. I've worked with a lot of people over the years who were 'so so' or even 'not particularly good' at their jobs, some of them very well paid. Very rarely did any of them get summarily fired for it. The NFL is a brutal workplace with expectations that are always unrealistically high with only so many jobs. The coaching fraternity is tight and supports each other for that reason most of all, maybe deservedly so.