Of course they train free throws, but good shooters won't need much free throw training as bad shooters.
You think Ray Allen trains free throws a lot? No he's naturally a great shooter and doesn't need to practice free throws too often, as much as a bad shooter.
in buzzerbeater every player is a talented free throw shooter, because you don't need to train it often to get solid averages ;)
And i wouldn't wonder when Allen would made tons of free throws, before he entered the NBA compared to other players.