Here's a quick civics lesson: Laws are made by Congress. The FAA operates under rules developed under laws passed by Congress. For example, the reason that a 333 exemption requires a pilot certification is because Congress failed to include authorization in the Act of 2012 allowing the FAA to exempt that requirement. The FAA is not autonomous. The White House is the Executive Branch. The White House enforces what Congress passes.
As I recall my civics lessons the Constitution clearly states that anything not expressly spelled out in legislation has no basis in law. Your remark that states "Congress failed to include authorization in the Act of 2012 allowing the FAA to exempt that requirement" is an incorrect assumption. The FAA could have made the exemption since they are empowered to formulate the rules on how to implement the Act of 2012. Since Congress gave no specific instructions on this issue FAA would have had the authority to add the exemption to the rules. Our history is replete with examples of Federal agencies bending the laws passed by Congress since they are left with the power to right the rules. Unfortunately our representatives have gotten extremely lazy and do not even bother to read the laws that their committees bring to the floor for votes so agency bureaucrats have a field day writing rules that benefit any number of political objectives of the Executive branch...