Re JGP’s comment: “Even if Paul doesn’t thrill you, whether it’s legitimate to lock him out is another question.” It probably wouldn’t be legitimate for the Republican party to do so; Paul is out-polling Thompson in New Hampshire, after all. The NH GOP was right to pull their co-sponsorship. But it’s perfectly legitimate for Fox News to invite whoever they want to appear before the cameras they own, as Ron Paul himself ought to agree (at least when he’s not ditching his principles).
Nobody is questioning Fox’s legal right to have whomever they please on their debate. As a libertarian, I also endorse Ted Haggard’s legal right to buy crystal meth from the male prostitutes he patronizes. But sometimes people—or journalistic institutions—implicitly hold themselves to more stringent standards than property rights impose. (And, indeed, “legitimacy” in political theory is often conceptually distinguished from “justice” or “right”.) All sorts of things that are within ones rights as a private citizen are outside the bounds of what is legitimate by the norms of a particular role one occupies—in this instance, the norms of journalism.