It is true. I'm surprised so many people don't seem to know this. This is such common knowledge that the onus is on you to prove otherwise. I suppose they want to sell suspense. Maybe they should show a video recording of it, publically, later. I just don't see how someone can actually believe a conspiracy with so many team witnesses watching the draw live.
HP is correct (wow, that really sounds weird to say). The actual Lottery procedure will take place in a separate room prior to the national broadcast on ESPN with NBA officials and representatives of the participating teams and the accounting firm of Ernst & Young in attendance. http://www.nba.com/warriors/news/inside-2012-nba-draft-lottery