I think you have the wrong impression of what stat geeks are trying to do. Baseball stat geeks do not go into anything with the intent of proving 'their side'. They do all of their research in an attempt to answer questions and to better understand the game, not to prove that traditional thinking is wrong. They would be just as satisfied proving that clutch does exist.
People have talked about the notion of clutch for a long time and have accepted it as a phenomenon that exists. Stat geeks want to see whether such a phenomenon indeed does exist by seeing if it can be quantified with any statistical significance. They are simply looking for answers.
To date, they have not found an evidence that clutch exists. At the same time, they have fully acknowledged that they have not proven that it doesn't exist. They are not going to accept that clutch exists simply because people say that it does. At the same time, they are not going to accept that it doesn't exist when they haven't proven that it doesn't. And so, they will keep trying to find the answer.
If clutch exists, it will be measurable through the player's performance.