It's weird how team defense oscillates between being vastly underrated and vastly overrated.
C's defense is not schematically and conceptually very different than, for example, Pacers' defense (or the defensive scheme O'Brien ran when he was in Boston). It's a "controlling the paint, sagging off, allowing post players to shot from the perimeter and rebounding" defense - Dick Harter perfected it in the NBA. The players make the difference; players skills and how well they execute. In this sense, team defense is very overrated.
Thibodeau is a great defensive coach not because he created some kind of genial defensive scheme; rather because he can identify the type of defense that fits his personnel, he can "sell" it to the players - and this is really hard to do -, he can make great in-game adjustments (like playing Garnett as a centerfield against Cleveland or a box-and-1 against LA), he knows what kind of drills that can help the team to improve and he can develop a player's individual defensive skills - like closing out on shooter with "high hands". Also, great team defense is very much a product of chemistry and chemistry is very much a product of coaching. Schemes are not that important: if Thibodeau was in Phoenix, he wouldn't have engaged in the same defensive team concept, because Shaq and Amare are not Garnett and Perkins. And Phoenix's defense wouldn't be nearly as good as Celtics' one.
You need players who are capable of speaking while they play (a very underrated skill), you need to keep all guys accountable, including the huper-duper-superstar - the only way of making them trust each other -, you need to motivate them to play defense- making guys like Pierce or Allen give up their bodies to take charges, not only in games but also in practices: there's no way of improving a defense if you don't train as hard as you play. And you need guys who are natural good defenders, with solid defensive fundamentals (the always underrated fundamentals). Replace Garnett with Amare, Pierce with Carmelo or Posey with Walton and our defense wouldn't have been nearly as good, even with Thibodeau in the bench. You can have great defensive concepts but if your post players tend to bite fakes, there's nothing team defense can do. If you don't have guys who provide quality individual defense, the rest of the team will have to play so much help and recover that will eventually totally wear down physically. If you don't have guys who are fast enough to play transition defense, you'd better settle for a very slow tempo and crash the boards.
In the end, it's the individual talent makes the scheme work, not the other way around. Having a player who recognizes and follows the rules set up by the staff on a consistent basis is very useful, but that alone doesn't make a great defense (at least not in the NBA, where every team can easily destroy a zone). Phil Jackson can define that whoever is guarding Pierce in the perimeter, must force him to the middle, where your help is, or force him to go to the baseline or whatever. Radmanovic can try to do this consistently. Consistency is important because it makes rotations easier to the other players - they know what's probably going to happen. But if Radmanovic isn't able to force Pierce to do any of those things, his teammates will have to overhelp too quickly and not going where and eventually the defense will become a mess.
The triangle offense is also very overrated. I wouldn't say that the triangle "has been totally dominating the league". How many teams without a combo of Jordan/Pippen or Shaq/Kobe were NBA champions running the triangle as their primary offensive scheme? Triangle offense apologists would say that the problem in this series was not the scheme, nor the Celtics' defense, but the execution. Well, this is kind of true to any "read and react" offense. The same can be said about a "double-drive motion" offensive concept. But players are not flawless, and it's nonsensical to assume otherwise. I have a few ideas why the Lakers' triangle didn't work very well, and I'll try to get back at this after watching Germany destroying Turkey in the 2nd half.
A last thing, though. Red's coaching philosophy was quite simple: you ask your players to do what they can do, not what they can't do. For example, it doesn't make sense for a team like the Celtics to run the triangle offense as their primary scheme because Rondo can't shoot. This is why Doc quit Rondo when he refused to take open shots or quit Powe when he fell in love with gambling in the passing lanes instead of rotating properly or it's stupid to want Garnett to play in the down block at all costs, like many fans want. This is why Red started running the fastbreak when he got Russell: he was great in the shot-blocking, rebounding and making the outlet pass (another underrated fundamental). This is why I can't understand why Phil stayed with the triangle when he had guys like Farmar, Ariza and Turiaf simultaneously in the pitch. After all these years, Red's philosophy still works fairly well.