Was Paulie being a "double agent" of sorts, playing both sides of the fence with New York and New Jersey a capital offense?

Consider his courting Johnny Sack resulted in two instances of Tony losing a good chunk of change, very nearly caused the murder of a fellow Capo, which in turn almost caused a hit to be put on Carmine, Sr., and in turn caused an (aborted) hit to be put on Johnny Sack. His betrayal marked the beginning of the deterioration of the NY/NJ partnership.

If I was Tony, a guy like Paulie, who already squawked to NY because he felt undervalued, is a liability. Sentimentality or no, he'd have to go.