IMO, it only starts to get really messy when you start mixing public and private funding. Example: A rule about prohibiting certain types of discrimination from health insurance companies vs. a publicly funded option. As you said, various health insurance companies can still compete around the same set of rules, etc. It may affect some of the economics of who can afford to play the game, and how they play, etc. but it's still pretty fair. Compare that with a publicly funded option that by virtue of its ownership does not have to weigh the same risks or set it's prices by the same rules, or even worse: one that wins what is essentially a government-enforced monopoly. Suddenly not so fair for private companies to compete against it.
