The main reason for the poor rebounding is because often times we're out of position due to our defensive philosophy when it comes to defensive rotations. Our defense is great, but sometimes you're going to give up a few things when you rotate as hard as we do in order to contest every shot. If we gave up a few more open looks, and instead sagged back, our rebounding would go up, but so too would our opponents FG%.
I understand your argument, but I'm, not sure that I buy it. Good rebounding and good defense aren't necessarily mutually exclusive:
Chicago (1st Def. Rating, 1st eFG% allowed, 8th DRB%)
Celtics (2nd Def. Rating, 3rd eFG% allowed, 11th DRB%)
Hornets (3rd Def. Rating, 4th eFG% allowed, 2nd DRB%)
Heat (4th Def. Rating, 2nd eFG% allowed, 9th DRB%)
Magic (5th Def. Rating, 5th eFG% allowed, 1st DRB%)
Bucks (6th Def. Rating, 6th eFG% allowed, 3rd DRB%)
In other words, it's very possible to both hold opponents to a low eFG% while also controlling the defensive boards; the top three defensive rebounding teams in the league all rank in the top six in defensive rating. Notably, the Celtics aren't terrible in this category, but there definitely is room for improvement (which will hopefully come with a healthier team.)
The lack of offensive boards may have more of a correlation with good defense. Only the Bulls and Lakers are in the top ten in both offensive rebounding percentage and defensive rating.