Legitimacy in RP doesn’t come from game mechanics or whitelists. It comes from RP.

Sometimes when something doesn’t exist in RP it takes someone who pretends to have already established it to get the ball rolling. The first cops in an RP server aren’t cadets because there would be no one to train them. Someone has to lay the foundation, and that someone just kind of shows up and says “I am” and expects people to go along with it.

The FIB is a federal agency that in-universe derives its power from outside Los Santos. Therefore, to establish it, someone had to just show up and say “I am” and expect people to play along, because that is what RP is all about. That someone was Bench Guy.