This is an issue, because of the way that benching starters has become conventional wisdom over the last 25 years. In fact, the foul out rate is down over 40% during that period (http://www.pistonpowered.com/2010/12/nba-players-are-fouling...).
So on one hand, yes, playing a starter in foul trouble could cause them to be less aggressive. On the other hand, I suspect there is VERY strong cultural bias that magnifies this.
I would imagine that an NBA team that has either veteran players or a very strong culture of understanding advanced statistics would be able to play as well when in foul trouble. (Think San Antonio, Boston, Dallas and Houston). I would also imagine that the evidence would not be as strong when looking at other time periods.
So it's an interesting observation, but it makes sense that coaches approach this issue on a case-by-case basis. Play Tim Duncan, bench Blake Griffin.
Also, the paper reads like academic research, but the layout and citations look rather simple. What gives?
EDIT: Their data source is listed, skimmed over it.
Looks like he has quite a bit of credentials and a huge interest in basketball. Very impressive.
We use a large dataset of play-by-play NBA data to determine when yanking foul-plagued starters is optimal by applying insights and tools from finance. We find that a team performs significantly worse if a starter with foul trouble is allowed to remain in the game, and that this effect is strongest in the third quarter. We use a novel win-probability technique that is sufficiently general to be useful for other questions simply by appropriately redefining the state variables. Thus, our two contributions are to introduce the new approach and also to demonstrate its usefulness by solving the problem of early foul trouble that had remained unaddressed in the academic literature.
Basketball games and seasons are very long. Players won't be focused in the entire season or for entire games. Having a deficit to come back from, with the time to do it, gives them a clear objective to focus in on.
But the other guy also correctly deduces the real issue... foul problems change how you play. You play more timidly. And I think it also results in the other team playing a form of basketball that is generally more desireable, which is to drop the ball into the blocks and try to draw a foul (its generally big men who get in foul trouble quicker than guards).
With that said, I think seeing this result is useful.