The same math holds true for the media. As a general rule, news doesn't become real news until the New York Times or the Washington Post report on it. After that, television and local news jump all over the story. (The exception is celebrity and gossip stories that have little importance.)
The government would be easy to control if you and your buddies controlled both the economy and the news. I don't see any elected officials being part of the illuminati. They would be puppets just like you and me.
My best guess is that 20 individuals could control the United States behind the scenes if they were the same people who controlled the financial markets and the media. And when I say control, I don't mean micromanaging things. They wouldn't care who was on the Supreme Court, for example, or whether abortion is legal. All they would care about is increasing their power and wealth, which are two sides of the same coin. So their interests would include wars and financial markets and access to natural resources. Everything else they could buy.
I'm not suggesting the Illuminati exists, or that the companies in the physicists' study are doing anything inappropriate. I just think it's interesting that the Illuminati is entirely feasible, bordering on simple. The CEO of any one of the big financial or media companies could pick up the phone and call a meeting of the others. Add some hookers and cigars and you have the Illuminati.
If you were one of the 20 powerful people, would you make that phone call and organize the others?