I'm a perfect example that there is no correlation. I got a 30 on the MCAT, which I think is mediocre. I even took a Kaplan Prep class.
On both my USMLE boards (Step 1 and 2), I achieved scores above 240. At the time (a few years ago), my scores were about 2 times over the standard deviation. I only used "First Aid" as my study guide.