All it takes to make the perception that the lottery is fixed go away is to put two sportswriters in the room for the whole process -- one from ESPN, one from a competing and independent company (CBS, SI, Yahoo, etc.). Let them watch the whole thing. Let them write what they see.
The fact that Stern doesn't do something as obvious and simple as that when he knows that everybody worries about the lottery being fixed tells us that yeah, the lottery really is probably fixed.