Yes, but let's be more clear about this...
The station started life at a time when the Cardassians controlled the Bajoran sector... it was constructed and deployed as part of their mission to strip-mine the planet and just generally oppress the fuck out of the Bajoran people.
When we talk about "Deep Space Nine," we're really talking about two different things.
1. The physical Nor
-class space station asset, of Cardassian design and... umm... Bajoran slave construction (per Sisko), is owned by the Bajoran government; at the end of the Occupation, it was abandoned by Cardassian interests, presumably captured directly or indirectly by the Resistance, and at some point handed to or otherwise defaulted into control of the Bajoran provisional government.
2. The Starfleet posting "Deep Space Nine" does not come into existence until after an initial treaty is formed between Bajor and the Federation.
Per Sisko, Picard, Kira and others in "Emissary," the agreement between the Federation and Bajor consists, among other things, of the following:
- Federation aids the Bajoran People
- Starfleet administrates the space station (thereby deploying an outpost)
Remember that all of this occurs before the discovery of the Wormhole, and just for those not keeping track, remember that at no time during the series itself is Bajor ever an actual "Member" the Federation... Bajor is a sovereign ally or protectorate state, but not part of the Federation proper.
The agreement between governments is advantageous to the Bajorans, because they are starving and in disarray and in any case couldn't defend (or even internally secure) their own sector, or administer the Station (a valuable asset) on their own.
This agreement is advantageous to the Federation and Starfleet because (aside from allowing them to generally be do-gooders and feel good about themselves for helping the Bajorans), the Bajor sector is strategically important because it is close to Cardassian space and the DMZ (and later because Wormhole).
The station remains "owned" by the Bajorans and is Bajoran "territory" (it is also said variously throughout the series that businesses and civillians onboard are subject to Bajoran law rather than Federation), there is a Starfleet intstallation of personnel and materiel deployed onto the station, and that assignment ("outpost") is called "Deep Space Nine." Part of whose duties, of course, are to maintain and defend the station physically.
Note that later physical upgrades and, critically, weapons emplacements on the station remain under the control and property of Starfleet (to the point they are deliberately sabotaged before the Bajoran civil siege in season 2 and prior to the Dominion annexing the station at the end of season 5). One would think that Starfleet substantially arming the station is allowed subject to the terms of some defence treaty with Bajor (probably an amendment to the initial treaty).
The command structure of the Starfleet outpost, its day to day operations, staffing, and chain of command are all going to be under the control of the Commanding officer assigned by Starfleet (in this case Sisko), subject of course to Starfleet regulations in general, and subject also to any specific standing orders from Sisko's direct superiors in Starfleet.
For example, this means Sisko can assign his staff as he bloody well pleases at any time... Now, conjecturally, the agreement between the two governments may indeed specify that DS9's staff must consist of, for example, minimum 40% Bajoran Militia members or something along those lines, and this could be enforced as part of the Sector's general orders. Very largely, however, all of that is completely under the control of Sisko. Recall that when he meets Kira, he does say that he "asked for" a Bajoran first officer / liaison officer.
Now. Enter the Defiant.
DS9 and the Defiant are, from a technical standpoint, two completely independent command structures, with Sisko assigned as commanding officer of both.
It is well-established in Trek (and in Naval tradition) that the chain of command in any Starfleet command structure, whether it is a starship, space station, or planetside base, while it is generally
determined by rank (by default), it remains at all times completely at the discretion of the commanding officer to unilaterally adjust the chain of command as she, he, or they see fit and for any reason.
Starfleet Officer or not (in this case, not), if we see Kira acting as First Officer of the Defiant, or even commanding the Defiant in the case of Sisko's absence or incapacitation, it is precisely that way because Sisko says so.
Nobody can override him, except his superiors in Starfleet (after the fact) if they have some sort of problem with it or if shit goes south on a mission and draws scrutiny and she (and by extension he) get blamed for acting inappropriately.
I would venture to suggest that none of the superiors higher up in Sisko's command structure have ever had a problem with Sisko's senior staff choices. Ross, for example, seems to have great respect for Kira in particular... and in any case, to have flag officers micromanaging the local commander's staff assignments is generally not something you see unless something is overtly wrong. Look how pissed off Picard was with Dougherty in Insurrection for what happened with Data. A better example would be when Nakamura initially reassigned Data from Picard's staff to become Maddox's guinea pig... or when Admiral Kennelly forced Ro onto Picard (although that turned out for the best).
Take Voyager (please, hur hur). Chakotay's crew consists of civillians, failed starfleet cadets, and a combination of retired/disgraced/AWOL Starfleet officers. None of the Maquis (save Tuvok) have current Starfleet Officer priveleges. When Janeway makes them members of the crew, she does it as a two step process:
1. Field commissioning general rank authority (making some "officers" and most "crewmen"). This is how Chakotay gets to be a Commander, B'Elanna a Lieutenant, and so on.
2. Specifically assigning individuals to particular points in the chain command. This is how Chakotay becomes the First Officer, and how B'Elanna becomes chief of Engineering.
Note in particular:
- B'Elanna received her provisional rank *before* the job assignment came.
- The Doctor is assigned CMO even though he does not carry rank.
- Seven of Nine is assigned as department head of Astrometrics, which has shown on occasion to include authority over other crew people working there, even though Seven does not carry rank.
- Back to a TNG example, Wesley Crusher is assigned to lead a geological survey team (which included full Starfleet officers) in "Pen Pals" even though he did not carry any rank at that time.
What it all comes down to here is that a Captain's word, on their ship or station, is God.