You can't fire a faculty member because outside the scope of his duties he expresses an opinion you don't like -- even if it's a clearly crackpot opinion. If you could, Stanford would have kicked Linus Pauling out when he became a Vitamin C crackpot.
The difference, though, is that Pauling was a sincere crackpot -- brilliant people are often susceptible to crackpottery because they're so used to being more right than their neighbors. Dr. Oz is a snake-oil salesman; when he's faced with people who are educated -- not necessarily scientists but critical thinkers -- in a forum he doesn't control, he speaks in a much more equivocal fashion. That shows he knows the language he uses on his show and in his magazine is irresponsible.
So selling snake-oil isn't crackpottery, it's misconduct. But somebody's got to find, chapter and verse, the specific institutional rules of conduct Dr. Oz's misconduct violates. There will have to be due process, particularly if he's a tenured professor, which will probably require lesser disciplinary measures than dismissal be tried first.