When I played ball (many years ago), I did pretty well at the free throw line. I made around 83% each year of high school. While I was at a gym a few months ago, I decided to shoot some free throws for the heck of it and I made 8 of 10. Granted, it wasn't in front of 15,000 screaming fans, and it wasn't immediately after running up and down the court for 20 minutes.
To me, free throws are mainly muscle memory - minimizing all unnecessary movements and using the exact same motion and follow through, never missing right or left, but occasionally missing short or long. It just seems strange to me that some of the best players in the country struggle so much in this area.