My take on it has always been this: Fleet Operations and Starbase Operations are separate -- individual Starbases can serve as headquarters of fleets and wings, but when they are not assigned as such, they are separate resources. Deep Space 9 would occasionally serve as an ad hoc staging ground, but was not the assigned base of any fleet. Therefore, it was separate. Individuals of sufficient rank and authorization could force Sisko's compliance with their fleet operations, but you saw that in at least one ep, when Sisko though Necheyev was jerking him around, he was *remarkably* free to give her his opinions on the subject, more so than a subordinate officer would normally give.
So my ruling, as a gm-writer, has always been that when the base in question is not formally assigned to the support of that specific fleet or wing, and the fleet or wing is more like an ad hoc task grouping, the captain of the ship best able to deal with the reason for the task force's existence becomes the ranking officer of the fleet (a la the rule about battleworthiness, as cited by Janeway to Ransom), and *requests* but cannot *demand* the compliance of the starbase commander. That starbase commander would normally not refuse, of course, but would not be a puppet, either.
In short, make it so that the players *can*, when your story demands it, take over the situation. But also make it so that there are roadblocks when they cannot. I can vouch for how well this works. The PC CO in our 3-year-long biweekly campaign (Episode 70 soon forthcoming) has had to deal numerous times with recalcitrant starbase commanders and colonial administrators, *except when I feel it detracts from the plot*.
Let the story always be your guide. To do anything else is to wargame rather than RP. And while I think most of us have nothing against wargaming, we like to keep it separate from our stories. 
BJ
"Every subject's duty is the king's, but every subject's soul is his own." -- Shakespeare, Henry V