Yup. That's the level I suspect these guys deal in. I'll share one personal vignette with Nicklaus that illustrates his way of thinking. During the '86 Open at Shinny, Jack was watching his son, Jackie finish up a round at NGLA late in the afternoon. He was sitting in a cart, and I went up and introduced myself and we started chatting. His son had recently been put out in the first round of the British Amateur by the eventual winner. My comment to Jack, Sr. was to the effect that at least his son lost to the winner - at which point Nicklaus stared me down and said, with great clarity - "You don't ever want to lose."
This showed me a ferocity of competitiveness way beyond any I'd encountered as a good college athlete. He just flat stared right through me and set me straight. So yes, I suspect Nicklaus would demand that Tiger sink as many clutch putts to win as many majors and that Tiger would agree on those criteria.