The problem was that there was no actual shift from public to private after the fall of the USSR. 7 of the top ten largest corporations in Russia are still majority state owned.
What is needed is not some public-private corporatist arrangement, what is needed are strong property rights and rule of law. Such that the state can't just come in and set up drilling operations and take the revenue from that and keep it(or use it to pay off your fellow former KGB cronies or what have you), and in the case of mineral rights on state owned property that the revenue goes to the people(who are the rightful property owners in those cases, ie Norway and Alaska) instead of being wasted by a corrupt government.