Difference between JJ and Erickson, is they didn't come to Miami after being fired from their last school like Richt did. I'd say getting fired pretty much disqualifies him from being "elite".
So, would Bill Belichick not be considered an elite coach since he was fired?
How about Pete Carroll who was fired not once but twice (the 2nd time before he became head coach at USC)?
They would, but.....
That's 2 examples. It can definitely happen, but an overwhelming majority of the time coaches that are "elite" do not get fired.
Both were NFL examples. Can you name when it's happened to a college coach?
Belichick became elite when he lucked into one of the greatest QB's of all time, and Pete Carroll became elite by being the best recruiter of the last 20 years.
I always lean to the players/talent being more important than the coaches. So I think if Richt is bringing in top 5 type recruiting classes, he's more than good enough to win an NC here. But if we're bringing in top 15 type classes like we have been, he's not a good enough coach to make up for that talent gap. The talent he recruits will go further in determining his success than the coaching job he does.