Regarding the former....it's possible the incentives were not enough to alter performance and not just ignored. There are tons of psychological studies that demonstrate failed intervention strategies.
Regarding the latter...pay-for-performance incentives DID exist, as has been admitted by just about everyone associated with this scandal, and the evidence suggests these incentives WERE EFFECTIVE in reducing penalties and sloppy, reckless playing because GW financially penalized players who made big plays but got a flag on the play. Perhaps THAT was GW's motivation: to get players to make clean, penalty-free big plays.
Regardless, it's not likely that we will never know the answer as to why the Saints have below average opponent injury rates, as there are too many variables to consider. But as a social scientist, I would love to run an experiment to see if pay-for-performance pools are an effective motivational tactic and yield better, safer performances.