Then why are you asking for a term?
A Qun following Qunari can not be the Inquisitior. It goes against the Qun. That's why the limiter is in place.
Yeah, the Qunari wouldn't have Inquisitors, much like they don't have any Wardens, it's simply not a role that they have in their society. The closest would be an Ashkaari (one who seeks), but that would describe Cassandra than the role that the Inquisitor plays.
Plus, we're being assigned as the Inquisitor at the start of the game, whereas if we were subject to the Qun, we'd already have long been assigned a role that we were required to follow, one which we could not easily change, if at all. While Tallis both loses and regains her role and rank in Redemption, it's suggested that she never stops being part of the Ben-Hassrath, simply reassigned within the larger confines of that order. Much like how Sten goes from being a Vanguard to becoming the new Arishok, he's still in the Antaam and has simply been moved up the ranks to the head honcho.
Or more simpy;
A Qunari following the Qun could not be an Inquisitor.
A Tal-Vashoth could be an Inquisitor, but would not want to be one since they reject roles entirely.
And a Kossith could only be an Inquisitor if you dug up their bones and propped their skeleton up in a suit of armour, since anyone belonging to that society is ancient, dead and gone.
(They've passed on! They are no more! They've has ceased to be! They've expired and gone to meet their maker! They've kicked the bucket, shuffled off the mortal coil, run down the curtain and joined the bleedin' choir invisibile! They are an ex-Kossith!)

Did they? If so I didn't see it. I saw a link to the wiki, but that's it.
I'm not asking for them to be in the Qun at all. What I'm suggesting is that Bioware will leave the reason your Qunari isn't in the Qun up in the air for the player to decide, rather than locking it down to "you were born outside of it."
Well click on that link and read it, it's providing the answer! But if you won't take the wiki for it's word (and hey, wikis can be edited by anyone, so I understand any reticence on your part) that poster also provided another quote from the developers saying exactly why you're not a member of the Qun.
That quote is already in this thread, just go back to the previous page.
We don't have to come up with any reason when we're starting a new game, Bioware has kindly given us one already.