At the 25 minute mark, he discusses the 2015 omnibus bill whereby the President can stop oil exports - and possibly refined petroleum products. Here is an explanation:
The President retains the power to restrict exports of crude oil through the imposition of sanctions under the International Emergency Economic Powers Act (50 U.S.C. 1701 et seq.) or regulations issued under that Act (other than section 754.2 of the Export Administration Regulations), the National Emergencies Act (50 U.S.C. 1601 et seq.), part B of title II of the Energy Policy and Conservation Act (42 U.S.C. 6271 et seq.), the Trading With the Enemy Act (50 U.S.C. App. 1 et seq.), or any other provision of law that imposes sanctions on a foreign person or foreign government, including foreign governments designated as state sponsors of terrorism.
Then what? Many of our refineries are built to process foreign oil and not domestic, while much of our domestic production is shipped overseas to foreign refiners. Converting our domestic refineries would take a lot of money and time, neither of which we don't have.
Then there is the question of who pays for the gas? As it is an internationally traded commodity (@Griz882) who will make up the difference if domestic oil producers have to sell it for less than the traded price domestically? In other countries that do that the government subsidizes the price of gas, are we really prepared to do that?