I'm pretty sure at least one of the NBA coaches at Sacramento, or Chicago, or New Orleans knew the game of basketball well enough to teach him how to play D just as well, if not better, than coach K could. The fact that he still has such a problem with it probably means he just didn't care enough to learn. In that sense he is the reverse of Dwight Howard, who was always great on D, but never put the effort into truly improving his offensive game.
When JJ Reddick went to the NBA from Duke he didn't have much of a defensive game either. But JJ realized that he wasn't going to last in the league unless he reinvented himself as a player who could do more than shoot 3s. His D and other off the ball skills were developed by NBA coaches, not coach K.
Interestingly enough, in the history of the NBA no Duke player has ever won NBA Defensive POY. Good defensive players can come from anywhere. A lot of the guys on the list came straight from high school. Granted, most of the guys who win are centers who get lots of blocked shots. One of the few guards on the list is Gary Payton, who went to Oregon State...not exactly a basketball power.