One could just as easily say that private regulation was involved, in the form of Massey's insurers. They, too, failed... and had a profit-motive not to've. Either they dropped the ball and didn't inspect the facilities diligently enough to determine they were unsafe (or so much as read the government's reports on their client's many published infractions), or Massey found it more profitable to pay escalating insurance premiums and government fines while remaining operational than he did to shut down production temporarily to address safety concerns. My guess is the latter.
Besides insurance, I have trouble imagining how private regulators could do much about anything since they have no legal power invested in them to discipline anyone.
Private regulation works if the company saves money or profits by risk-management and self-regulation, but if a company is solely interested in short-term profits, sustainability and safety may no longer be priorities. At that point the only thing holding them back from pursuing gains by endangering their employees and facilities is ethical scruples, of which Massey appears to have had none.
The only agencies that have the ability to make regulation compulsory are the government and the insurers (for legal and financial reasons, respectively), and while I agree that they let those miners down in the gravest possible way, pulling the old "leave it to the market!" BS is as intellectually lazy and absolutist as saying government regulation is necessarily useless.