Thanks. What I wrote is simply Mob protocol: someone in a boss's crew is his responsibility. Allowing someone from outside the family to settle that responsibility is a mark of weakness.
In the film, both Jimmy and Henry were complicit in Billy Batts' murder. But Paulie didn't punish them. We might think that the reason was because Jimmy wasn't Italian and Henry was only half-Italian, so they were ineligible to be "made," and therefore couldn't be expected to live by the "rules," as Tommy was expected to. By far the more likely reason is that Tommy was a "cowboy," as Paulie explained to Henry earlier. He was wild, dangerous, not to be trusted. A guy who would kill a made man from another family in a personal dispute was a liability to Paulie. And, even more important: Jimmy and Henry were "good earners." Paulie needed the money they brought in.