ARod has not performed at his elite level in his career postseason, but his OPS of .844 is about the same as Jeter's and better than most and he has been excellent in the ALCS (a more clutch spot than the ALDS) with an OPS of 1.024.
Right. But, ARod's regular season OPS is .966 (vs .844 postseason). In addition, his regular season 2-out RISP BA is .272 over his career. Meanwhile, Jeter's OPS numbers are stunningly similar comparing regular (.845) and postseason (.846 post). For his career, he hits .320 with 2-outs and RISP.
You say it's been proven time and time again that there is no such thing as clutch players. To that, I say, you are relying way too much on inadequate measurements and not enough on common sense.
Of course there are clutch players, just as much as there are chokers in all sports. This is a psychology question, really. There are some people who have the mental make up to perform at and above their normal levels in crucial situations. By the same token, there are those who repeatedly perform consistently below baseline in the most important situations.
The reason you often don't pick this up is because the measurements we use or the definition of clutch situations is probably inadequate. But, it doesn't make any sense if you just take a step back to say that there are no individual differences between how certain guys adjust to increased amounts of pressure.