He answered your question. He said that everybody else reads the Times, and it's important to him to understand what everybody else is thinking.
I can understand his logic. Until clo kicked me off of her board, I had a pretty good balance of left-wing and right wing thinking. It turns out that left-wing thinking doesn't involve the brain, but that doesn't change the fact that it matters. There are as many left-wingers in our country now as right, and soon there will be more. Their ill-conceived "thoughts" are important to understand. Boards like Pope IV are not going to be much help with that.
So Stossel chooses to read the New York Times. As long as he is vigilant against the possibility of his own mind being warped by the experience, reading it is healthy. He'd better be reading some other things too, though, or he'll be making decisions and establishing viewpoints based on nothing but garbage.