Not that I'm likely to rely upon the FBI for my own personal protection...
... But they are supposed to be law enforcement officers and protectors of our society.
This isn't a Fortune 500 company secretary pool he's applying to join, where a larger computer monitor can help with impaired vision issues, or an alternate design mouse can help with carpal tunnel.
This is a job where physical danger is possible, rapid reaction time and combat skills may be necessary, strength and agility and full ambidextrous dexterity will be necessary, and other people will depend upon those capabilities.
If he can't perform the tasks of a paramedic/EMT, as well as operate a firearm, he shouldn't be a FBI agent.
I don't know the dexterity level of his prosthesis, but I doubt it would allow him to assist a paramedic team in the middle of an emergency situation. Or pick up a person in fireman-carry position without his prosthesis falling off. That would disqualify him if I were writing the requirements.