How do we know S31 isn't accountable to anyone? Because a bunch of their operatives said so? They're all known liars, and I wouldn't put it past them to use this "rogue elephant" story as a cover to protect their superiors in the government--pro-active deniability, if you will.
1. Sloan
wanted to recruit Bashir. If Section 31 really did answer to the Federation government, he would have said so to Bashir, since that was Bashir's primary reason for objecting to them and not joining.
2. That Section 31 does not answer to the government was confirmed in "Extreme Measures" when Bashir and O'Brien found out in Sloan's brain that Section 31 had an agent in former President Jaresh-Inyo's Cabinet. Let's repeat that:
Section 31 was spying on the President. They obviously aren't accountable to the government if even the President himself can be one of their victims.
Perhaps Starfleet Intelligence even drew upon the legend of the 22nd century Section 31, constructed an elaborate mythology around it, and impressed this mythology into memory implants for certain high-risk officers. When your potential enemies have mind sifters, telepaths, etc., you need to overwrite your operatives' memories if you want any chance at maintaining plausible deniability, and the rogue agency story has its uses.
There is no evidence for this, and the information inside Sloan's mind directly contradicts it. And, as Bashir noted, it would have taken more than one or two agents like Sloan to create the morphogenic virus that was destroying the Founders.
MI6 are a foreign intelligence agency also. MI5 operate internally.
So...outta curiosity, what are the duties of MI1 through MI4? And is there an MI7 (as M in "Dr. No" implied)?
MI5 and MI6 are unofficial names for the
Security Service and the
Secret Intelligence Service. The MI Numbers refer to the
Directorate of Military Intelligence, a division of the War Office that existed until 1964. During World War I, the Directorate was divided into different section numbers -- so, for instance, the Secret Intelligence Service started out under the official name "Military Intelligence, Section 6," etc. The MI numbers are no longer in effect, but MI5 and MI6 retain them unofficially.
According to Wikipedia, some of the divisions included...
MI1: Codes and cyphers. Later merged with other code-breaking agencies and became Government Code and Cypher School (now known as Government Communications Headquarters).
MI2: Information on Middle and Far East, Scandinavia, USA, USSR, Central and South America.
MI3: Information on Eastern Europe and the Baltic Provinces (plus USSR, Eastern Europe and Scandinavia after Summer 1941).
MI4: Geographical section - maps (transferred to Military Operations in April 1940).
MI5: Liaison with Security Service, following the transfer of Security Service to the Home Office in the 1920s.
MI6: Liaison with Secret Intelligence Service.
MI7: Press and propaganda (transferred to Ministry of Information in May 1940).
MI8: Signals interception and communications security.
MI9: Escaped British PoW debriefing, escape and evasion (plus enemy PoW interrogation until December 1941).
MI10: Technical Intelligence worldwide.
MI11: Military Security.
MI12: Liaison with censorship organisations in Ministry of Information, military censorship.
MI13: Not used (except in fiction).
MI14: Germany and German-occupied territories (aerial photography until Spring 1943).
MI15: Aerial photography. In the Spring of 1943, aerial photography moved to the Air Ministry and MI15 became air defence intelligence.
MI16: Scientific Intelligence (formed 1945).
MI17: Secretariat for Director of Military Intelligence from April 1943.
MI18: Not used.
MI19: Enemy PoW interrogation (formed from MI9 in December 1941).
MI (JIS): Axis planning staff.
MI L(R): Russian Liaison.