[Well, it's a relief that Ezio wasn't lying about the entire thing, at least. This still sucks, though.]

... Between Mr. Auditore's confession—about how Mr. von Karma was corrupt—and how Higekiri knew that the man was on death row, there's something we can probably assume at this point.

Seems like the Bandits are told some personal info about their targets. Reasons to kill them, specifically.