It's not your oil any more than the PF is . The oil belongs to the state ...12.5% of it anyway per terms of lease agreements. The oil wealth(which creates the PF) and the Permanent Fund and collectively or communally owned resources. They are not individually owned. Therefore the wealth has to be controlled by the government and that's where the confusion lies. 
The good news(or not so good news) is that the people in theory are supposed to be in control of this government....you know - of, for and by "the people".