Hasn't worked that way in the past. I was working in the oil business in Indonesia and knew production people in Pertamina (the national oil company). When world consumption decreased and OPEC raised prices the Indonesians started understating the quality of their oil, usually by classifying it at a higher then benchmark viscosity - high viscosity oil sells for less then light-sweet benchmark oil.
Many of the oil exporting nations depend almost entirely on the income from petroleum so if demand decreases many of them immediately act to increase sales.
John