Even the FBI admit Kuklinski was a liar
That he was completely full of crap about a lot of the crimes he claimed to be in on and stories he told.
He claimed he was DeMeo's most trusted killer; practically every Gambino hitman and crook who turned snitch claim they either never saw him, or he was just a rent-a-goon. He claimed he killed DeMeo when its widely accepted "the Gemini Twins" did it.
Kulinski was a killer, no doubt, but he knew he'd die in prison so he made up a bunch of bs and exaggerted lies to entertain himself and build up a small legend.