Probably because FBI work is just as repetitive as Accounting
Actually, i think this is partly right. Going through boxes and boxes of documents can be extremely repetitive, so they want people with experience in it who can handle it and detect minute details that might be important.
But you don't NEED an accounting degree... other degrees with get you into other fields. Psychology will get you into a field working with people... medical and you'll be doing autopsies... criminal and you'll probably work in the field... a CS will probably get you working in the computer division, etc, etc.
The FBI also handles all cases of counterfit money making in the US
You sure about that? I'm pretty sure the Secret Service handles that.