Jim, you don't think that Jack worked on his short game? I'm pretty sure he did everything possible to be the best player, be that putting practice, bunker practice, or whatever it took. That doesn't mean to say he was a great chipper or bunker player but who's to say he could have been any better than he was?
As far as his putting is concerned, he was simply one of the best 'clutch' putter of all time along with Woods. Putting is still part of the shortgame.......
Mike, we had a pretty extended discussion of this a little while ago, in a Michelle Wie thread of all places. Jack said he didn't practice his short game much,and wishes he had practiced more. Phil Rogers, who coached him, said Jack had great touch but not many shots. Jack said, I think, that he used sand wedge for 95% of his short game shots. He also said things got so bad in 1979 that he was afraid to pitch over bunkers: he was nearly putting/chipping around them.
Rogers gave him some short game lessons in early 1980. That helped him win two majors that year. Still, he only got up and down 31.4% of the time from bunkers that year. Really bad, by almost any measure.
Jack was a great clutch putter, true. Most of us, including me, separated putting from the rest of the short game. And if his short game had been great, instead of maybe average, he wouldn't have needed so many clutch putts late in the day. He would have put away the tournament long ago, much like Tiger did when he was best at long game and best at short game.