There's absolutely a common misconception in which people believe certain players are capable of radically outperforming their talent level in high leverage situations. However, everyone reacts to feeling pressure differently, falling somewhere on the spectrum between utter loss of focus and becoming "dialed in". I don't think it's crazy to believe these changes in mentality can impact performance.
Additionally, no one player reacts uniformly to pressure across various instances. For example, a hitter normally crippled by these situations may react better during a hot-streak or time of increased self-esteem due to recent non-baseball related events (banging a supermodel or something lol). Another factor could be how a hitter reacts to pressure relative to the current pitcher. For example, a hitter who thrives under pressure may face a pitcher who actually reacts better, thus varying the outcome expectancy.
I believe "clutchness" is definitely a factor, it's just not nearly as simple or impactful as it's made out to be.