Line officers, too, I think? That's the old chestnut: who's who in "Court Martial"? Two guys wear a green dress jacket, one has a blue one. There is no discernible difference between a Commodore's dress uniform and a Captain's. The titles up for grabs are "Space Command Representative Lindstrom", "Starship Captain Krasnovsky" and "Chandra".
I'd be willing to make the green-jacketed guy to Stone's left Krasnovsky - he looks Russian enough for the "narrow ethnicity view" to work, too. The other green Captain or Commodore could be Chandra, again by ethnicity. The blue jacket would then signify something other than starship command; a "Space Command Representative" might be Kirk's peer but might never have sat in the center chair of a Starfleet vessel.
But Stone seems to nod the other way, indicating that Lindstrom is to his left, in green. No problem: the other green guy can be Captain Krasnovsky, despite the ethnicity mismatch, and the blueshirt Captain or Commodore can be Chandra, a guy apparently so famous that his exact title and role in Starfleet need not be mentioned.
So no need for any of the non-greenjackets there to have a starship CO past, really.
Going from command colors to something else is pretty rare in general. But it happens. Happened to Spock after "Where No Man". Happened to LaForge and some other low-ranks, too. Could certainly happen to Stone.
The question is: Was Stone the commander of a starship or a Starship?
In the TOS context, I'd have to say Starship. I wonder if there's something in Stone's past that forced him to relinquish Starship command and accept a desk job - thus making his eagerness to smoke Kirk out of his command all the more poignant?
Timo Saloniemi