A couple large problems with that article:
1. ESPN's "In the last 24 seconds" includes all sorts of ridiculous shots with little/no time on the game/shot clock from all over the court. Comparing the field goal percentage of those shots to regular shots is meaningless.
2. The 82games.com stats may also be misleading, as clutch FG% should be compared relative to the change in league average field goal percentage in close games (relative to the rest of the time). That is, at the end of close games, when defenses tighten and more low percentage buzzer beaters are shot, team field goal percentage undoubtedly goes down. Based on the analysis, if a player's field goal percentage decreases by less than league average in clutch situations, he's not clutch, even if, as stated in point 1, he's taking a bunch of deep, well defended buzzer beaters. The analysis has been rigged to produce the desired result.
To correct the study, you need to define clutch possessions, and then look at league average expected points by possession type on those possessions (possession type would include scoring margin, time remaining on shot/game clock when the player receives the ball, where the player receives the ball and what play type is used). Do the same for non-clutch possessions. Then, calculate how each player does (points per possession) in both their clutch and non-clutch possessions (for each possession type already mentioned). How does the player do relative to league average? How does his performance drop-off relative to league average?
It might also be worthwhile to look at team performance with certain players on/off court in clutch v. non-clutch situations.