I recall a mid-major team that finished last and led their league in rebounding margin (which is where you need to look - the total number of rebounds is more of a reflection of tempo).
A few factors can be involved in that statistic beyond just simply being a good rebounding team (which we are not).
Odds favor the defensive team on the boards (70 percent or so). So - all things being equal - if more shots happen to be missed on one of the floor, that defensive team should have an advantage. Therefore, if you have a big edge in turnover margin, you may lose the battle of the boards, since those are shots your opponents never get to take. Our 1989-90 team was small and probably was outrebounded a lot, but our press was lethal.
Offensive efficiency is also important. If you shoot a terrible percentage, you are creating more defensive rebounds for your opponents (and if you allow your opponents to shoot a high percentage, you are creating less for yourself). A team like Princeton or Butler works at being efficient on offense and strong on the defensive glass to counteract their lack of an imposing frontline.
Defensive rebounds off missed FTs are the easiest to get (over 90 percent), so if you shoot poorly at the line, you give your opponents gimme defensive rebounds.
We know this all too well, but shot blocking can also negate some of your advantage. The guy going for the shot block is one less guy in defensive rebounding position, so the odds of cleaning up the boards go down. Shots blocked out of bounds or back into the hands of the shooter are offensive rebounds allowed.
Often, the rebounding margin in a specific game can be deceiving. You'd expect things to balance out over the long term, but the best way for us to overcome our rebounding deficiencies is to win the turnover battle with our strong guard play and get extra possessions.