well, this is 3 claims, really:
1: blowhard -- I don't think even his firmest defenders deny that the guy is a blabbermouth with a big ego. Beyond blowhard, the real problem with him is what a spinner/politician he is, constantly undermining those working with him. That takes blowhard in a very destructive direction.
2: outsize rep -- he's under .500 for his career and yet he still avoids criticism. There's only "firejohnidzik.com" even though Rex has been associated with this regime for much, much longer. This popular rep flows out of his popularity with the media, which has consistently ignored his role in the Jets' decline. One can parse forever how much credit a guy gets for the good (2 flukey playoff runs) and bad (a terrible run after he lost some key players), but bottom line no way his record is other than, at best, journeyman.
3: gifted on defensive side of ball: I guess tims4wins would agree with your claim some say he isn't gifted, but generally I think that's a bit of a strawman. My own call is that he does come up with some innovative defensive plans and can, at times, clearly a great motivator. So that = gifted to me. He has plenty of faults, though, even on the defensive side, so if by "gifted" you mean he deserves his defensive genius label, then no. He has gifts, but too many flaws, too.
The rubber hits the road in two ways:
1: should he replace MP as Pats' DC if he is fired? I say no way -- would be a disaster, and I think this points that he's "gifted but flawed, not "so gifted you must hire him." The same goes triple for being hired as the Pats' #2, as was suggested above -- that's pure insanity.
2: should he be hired elsewhere? As a HC only really as a PR move for a bad team. If I was Jacksonville and needed to get fannies in the seats I might hire him...but if I ever had players good enough to compete there I'd immediately fire him, too. As a DC, I could see more situations where he's as skilled or more than others so in the abstract he deserves those jobs....and is certainly qualified for them. That said, if I'm a HC or GM, do I really want him in house knowing what chaos he sows and how he can undermine those around him? Nope, but I could see a meddling owner -- in Oakland or Cleveland or D.C. -- overlooking that and wanting to bring in his outsized rep.