The Celtics of this past era were hardly ever a good offensive rebounding team. In fact, Doc Rivers made a point of de-emphasizing the offensive boards in favor of transition defense. Regardless of your opinion of that theory, it was his strategy and it happened to be favored by Greg Poppovich as well. Those are two pretty smart guys, so for the most part I'm happy to defer to them.
Now along comes another pretty smart guy, this one a writer, talking to front office folks around the league (we'll give them the benefit of the doubt that they are at least pretty smart), plus some MIT students (who by definition are smart and have access to new stats and tracking data). Zach Lowe goes into great detail in an attempt to debunk the theory that offensive boards correlate at all to transition defense. (Go read the whole thing because I don't have the time or energy to do it any kind of justice in this space)
But the available numbers suggest elite offensive rebounding teams fare just about like anyone else in transition defense. They’re average overall. Some are really good, and some — hi, DeMarcus Cousins! — are terrible. But there’s no obvious evidence that crashing the offensive boards is a death sentence for a team’s transition defense.
Lowe goes on to point out that the Celtics and Spurs also had two aging big men in Garnett and Duncan that have gradually moved away from the basket as their careers have progressed. So some of Doc's strategy has got to do with personnel.
Also, Doc never discouraged rebounders like Jared Sullinger from staying in the paint on shots in the air. He just knew that he didn't have many natrural born rebounders and his team played a lot of perimeter basketball which lends itself to long rebounds and quick outlet passes going in the other direction. He basically played to his team's strengths and then used his mantra to deflect criticism for his team's historically poor offensive rebounding numbers.
Zach's point is that you can indeed rebound the ball on the offensive side and still defend in transition well. The Pacers did both exceedingly well and won a lot of games that way. But they had the horses and right-minded folks to do it. The Celtics over the last several years have not.
So I think Doc and Zach are both right.