The oil part is true but why it is not Saudi real and why it is "trust in us government" is because USA basically owns Saudi Arabia that is why. Saudi Arabia could "try" to not give their oil to USA and try to blackmail USA and just sell their oil to Russia for cheap and that is exactly when USA will decide "bringing democracy to Saudi Arabia" is a good decision. It would be a bloody war again but you will see a USA flag everywhere in Saudi Arabia for sure.

Hence, Saudi Arabia just sells their oil to USA and lives freely with that money and do whatever they want. So, just because Dollar is backed by Oil doesn't really mean its also not trust to government, its basically hand in hand, you literally trust the government to find oil at all times no matter where and how.