[@KatherinWinter]

In the movies, the MIB was extragovernmental; they had no ties to any or organization besides their own and did not swear allegiance to any government. Their recruitment from other organizations was covered up by erasing all evidence those people had ever existed; "walk in shadows move in silence" as the song says. If we're based on the movie version, The Director likely wouldn't need to report to the FBI or the president; only the MIB, their parent organization.