It's just not that important ( as far as this particular team's strategy goes). What's more important is that we get back on defense and stop the other team from scoring.
Boston Celtics basketball under Rivers and Ainge has two basic concepts:
1)Slow the game down, execute the offense perfectly and get high percentage looks at the rim, exploiting certain match ups. Once we get that good shot, the most important aspect is to ensure that the other team doesn't get a high percentage shot. Don't worry about rebounding because if we can stop them scoring, we don't need to put an emphasis on rebounding as much.
2) Defend harder than anyone else. Deny the ball and force the opponents to take an ill-advised shot/possession-preferably a jumpshot. Get the defensive rebound and exploit their fast break defense with Rondo by consistently putting pressure on them to react to him- thus taking them out of their normal defensive patterns which ultimately leads to opponents mistakes.
The last 5 years has been about getting back on defense and stopping them from scoring. People say 'well why don't we rebound and defend together?'. It just doesn't work that way, it's not necessarily one or the other but you can't just weave the two together and create a perfect combination when your number one priority and strength is defense.
This past year, it was that defensive rebound that was an issue a little to often. Great defense can become average with to many extra shots.
It's hard to blame just our rebounding. I don't think our close out defense was as good in the playoffs- but we had Pierce and Ray running around on one leg trying to guard Lebron and Wade which made a huge difference. I think we are going to have to defend the 3 point line better than Chicago does if we really want to beat Miami. I think this is part of the reason Danny isn't too concerned with our size inside on offense, as long as we can effectively defend the Bulls big men then the Heat is a completely different ball game.
The Eastern Conference is turning away from playing though the interior/post so much and leaning more towards transition basketball with hard nosed defense that basically extends to half court.
I think one of the reasons Danny likes Sullinger so much is that he saw how effective Miami was with Lebron in the low post because of his passing ability. He backed his way in, and then found outside shooters or slashers very effectively and it completely dumbfounded OKC and us. People said before the finals that Lebron wouldn't be able to abuse Durant in the post because Durant was too long. Lebron manhandled Durant in the post by physically pushing him to the side. Once he scored a few times, it commanded an immediate double team and Miami had a field day from beyond the arc. Guys like Sullinger that can post up, stretch the floor and pass like Lebron are a hot ticket. We got extremely lucky to get this kid and once people see how many easy looks Pierce and Terry and Green get with him bulldozing his way in, then kicking it out to the above mentioned it will be a whole new dynamic to our team. Perhaps not immediately this year but eventually he'll be an assist machine.
He can also get his own rebound if need be much more effectively than Bass and even KG at this point in his career.
You are right that our rebounding is going to be tested again in the playoffs against the Bulls. I think Danny's answer to this is to sure up the bench and get role players that can come in and extend a lead, create their own shot, and knuckle down on defense, crossing his fingers that the same strategy works. It's hard as GM in the East to create a team that can compete with Chicago inside, yet is fast enough to get back and stop Miami from running their transition offense-whilst defending their three point shooting well. I think part of it is also just the plain fact that we couldn't really get any beasty rebounders in free agency without having to massively overpay or give them long term deals. It just isn't a huge priority compared to defense while we have a defensive core of Rondo, Bradley, KG and Green now.