And private entities are around to make money. Getting bribed is making money. Public regulators are there to, well regulate, and taking a bribe is not directly in their interests. Not to say that public regulators cant' be bribed (they obviously can), but I wouldn't trust a private regulator for much.
Especially considering the current corporate model, where the regulator would probably be owned by the regulatee. Seeing as how the way we currently know who owns what is becuase of income tax returns, it would become very hard to track the corporate influence.