it's not a myth, someone either pulls it off often or they don't.
but the point is that they tend to pull it off at the same rate that they would otherwise get hits. Obviously if there are going to be runs driven in from scoring situations or late in games or whatever someone's going to have to get those hits. But the question of clutch hitting is whether or not players are going to be more prone to doing so in those situations than they might be otherwise. And that's where the evidence tends to stand up against the notion. Derek Jeter has a rep as a clutch hitter, but that's almost ignoring the fact that he's a damn good hitter the rest of the time too. He's not suddenly any better in "clutch" situations than he is the rest of the time over the entirety of his career.
Obviously there are going to be some guys that show better clutch numbers and some that show worse. But often these are in part because of small sample sizes, and may very well be prone to wild fluctuations over the course of their career.
Just for JP, in 2012 he had his highest BA in situations with RISP, but it was also counted in only 1/2 the PAs as just having men on base (keeping in mind that the men on base stats incorporate the RISP ones) and 1/4 the PAs as the bases empty. (the #s were .235 for bases empty, .230 for men on base, .295 for RISP) In 2011 he was .193, .254, and .242 respectively.
Problem with JP is that it's a small sample (2 years and limited PA's in the RISP situations.) So what about the aforementioned Mr Clutch, Derek Jeter?
.304 with RISP, .308 with men on base (RISP or otherwise), .310 with the bases empty for his career. And year for year, the numbers fluctuate wildly. In 08 he hit .317 with RISP and just .300 with the bases empty. 09 he was just .259 with RISP and .359 with the bases empty. '10 had him at .271 RISP and .290 bases empty.
So the end result is that there are swings in his numbers from year to year with no discernable pattern, and that for the whole of his career he's slightly worse in RISP situations than bases empty (although in reality the range is almost statistically insignificant at .006 points difference.)
and that tends to be what bears out with most other hitters. Their "clutch" stats are going to be consistent with their normal stats on the whole, with swings and changes you'd expect to see with sample size problems in year-to-year stats.
EDIT: I should note that Fangraphs also tracks low, medium, and high leverage situations, which factors in runners, game score, innings, etc, and the same pattern emerges.