Yeah, you're not a random attendee to close rifts. You have your own army, spies, and everything. The Inquisition has its own troops, fighting mages and templars, and even your own commander that you can see fighting wearing that lion helmet. It's reaching to say that you're a random attendee when you have an entire chain of command.
Not in my version of the game. I am asked to help an established group close a tear in the Sky, then run around for a while helping their army, spies, etc closing rifts and whatnot based out of a place called Haven. Later, when a Darkspawn Magister named Cory chases us away, it is then I take up the mantle as a figurehead for said organization.
Now, in my games thus far I have remained humble enough in my new found title to continue to help those like the earlier folks in the Hinterlands, Crestwood, the Fallow Mire, the Storm Coast, etc. Thing is, by this time there are fewer folks needing stew meat and more requiring someone to chase the demons off of their property, but my Inq's are still willing to help.
Now that is how I have played my first three Inq's. However, I could play a less congenial Inq in the future and make different choices, seeing how this remains a single Player game. Options; gotta luv 'em....