I profoundly doubt that Section 31 is anywhere near as powerful or widespread as it likes to think it is. Contrary to the absurd fantasies of fiction, the bigger a conspiracy is, the more inevitable its exposure becomes, because there are more opportunities for things to go wrong, more lines of communication to be intercepted, more people who could have second thoughts or be co-opted, etc. The idea of a vast, all-powerful, pervasive conspiracy that nobody knows about is a contradiction in terms. The only way Section 31 could've lasted as long as it has and stayed as well-hidden as it has is by being small and limiting its activities.
So the tendency of some fans to assume that S31 has its talons in every single intelligence operation or ethically questionable action in Federation history is one that should be resisted. The problem with conspiracy theories is that they're based on the lack
of evidence for a conspiracy. When you're imagining an unknown menace, your imagination tends to run away and picture it as something huge and supernatural and unbeatable. Usually, if there's any real threat underlying the conspiracy theory at all, then the facts would show it's much less powerful, competent, and expansive and far more vulnerable.