I'd argue the opposite.
Cornwell: "The admirals who run Section 31 haven't responded to me in weeks. Their threat assessment system, Control, isn't accepting my data input codes anymore."
Pike: "Any idea who programmed it to shut you out?"
Cornwell: "Admiral Patar. She's a logic extremist. Frankly, I find her fanaticism worrying. Once the signals appeared, she started lobbying Starfleet to turn its decision-making entirely over to Control. Control is a great resource. Every Starfleet admiral feeds data into it.
We consider its recommendations."
A separate bunch of Admirals runs Section 31. Their rank pins don't put them beneath Cornwell; if anything, Patar appears to be a full four-laurel Admiral and thus outranks Cornwell. So these may be expected to respond to Cornwell, but they can't be expected to answer to her in the hierarchical sense.
The bunch seems a bit much for merely holding the S31 leash. Might be S31 is one of their chattel as part of the greater SF Intel community. But Cornwell is not one of the bunch.
That Cornwell is a user of Control services, and now shut out, merely puts her level with "every Starfleet admiral". That she knows a thing or two about S31, its forward operating base and so forth doesn't yet make her more an insider than the rest, either.
So far, Cornwell has done very special things indeed. But utilizing the unique
Discovery for unique missions is an artifact of the
Discovery, not of Cornwell. If the only way to conduct the Klingon war is via the
Discovery, then an admiral in general charge would use that asset, not just an admiral in specific charge of shady stuff. The one independently shady thing she did was help Sarek negotiate with the enemy in "Lethe", but that was only because she happened to be there...
Vice Admiral rank would qualify Cornwell for "sector command" in TNG era terms - the three laurels would match those of, say, Ross. Or Nakamura, or Rollman, or any of the bosses directly associated with a specific starbase. Then again, Vice Admiral is fine for "theater command", too, as with Haden who seemed to be the go-to man for Romulan affairs, or Nechayev who dabbled in everything relating to the Maquis and the Cardassians.
But Cornwell
could still be special ops if need be, keeping good company with Vice Admiral Cornell West from STVI:TUC...
Timo Saloniemi