Why did pussy pull Skips taffy?

This is a difficult issue for me. For over a year Pussy was a full fledged FBI informant and a captain. It never gets Tony or hardly anybody else indicted for a damn thing.

He encounters somebody he knows at a party place where he is meeting with Skip. Skip tells him it went off ok but Pussy goes to the guy's house under the guise of a social visit for coffee and murders him. So Skip would not know that was Pussy who murdered this guy? You have opportunity and motive staring him in the face not including any evidence at the scene!

Of course Pussy tried to play both ends at the same time but that is not easy to do and he was not that clever.