It's not a myth. Just look at Ortiz.
If we want to get into scientific stuff. A while ago in SI or ESPN Mag I read about this doc who studied athletes based on six different aspects of their personality type (Extrovert/Introvert, etc.). I think the doc's name was Jon Niednagel, but I'm not sure. Anyway he typed the athletes by their personalities and explained why it seemed certain athletes performed better under pressure (I believed he used Tim Duncan as an example). I came away from that article convinced that certain people perform better under pressure than others (I mean really, don't we all already know this?). Why shouldn't people's physical abilities get affected based on the pressure that they feel or put on themselves?
On a non scientific note. I was seeing this girl for the first time and her boyfriend showed up with about 10 or 12 of his guys. All I knew was when I saw them, I wasn't really thinking straight. Some guys I know freak out during test time. A buddy of mine can nail 50 FTs in a row but during the only 2 organized games in his life, he choked on the FT. I can shoot 3's all day by myself, but when the game is on, I even brick wide open shots. Pressure affects people differently. I don't see why it can't affect your ability to hit a baseball.
Also look at pitching. Armando Benitez is a great non pressure guy to have on the mound, but look at what happens to him every single time he is in a big spot.