It kind of reminds me of Mass Effect 2. You are working with Cerberus, but you can be opposed to Cerberus' will. Same here. Chantry funds you and gives you troops and connections, but you don't spread the Chant.
I think they want to avoid the Cerberus thing. What happened in ME2 was pretty straightforward: "work for Cerberus. And don't complain until the last mission in the game!". More options to complain would have been welcome, seeing that working for them was unavoidable. But what has been said until now doesn't mean that our choices won't benefit the Chantry in the end. Let's take DA:O and apply the quotes for Inquisition:
-"You're using your position and some of the things you do very early in the game to allow you to lead the Grey Wardens" (because you're one of the last two survivors and the other warden doesn't want the responsibility)
-"You lead them in opposition to the will of the Kingdom of Ferelden" (true, since Loghain is the official regent and Anora is the queen)
-"You're not a puppet of the king or anything like that" (the other way around: Loghain accuses Alistair of being the Warden's puppet)
-"If anything, you're the upstart rebel" (the Wardens become outlawed and take part in the civil war)
It fits, doesn't it? But in the end you saved Ferelden and, if the Warden survived, he or she became a feudal lord in the kingdom in the name of the Grey Wardens. Who's to say that the same or something similar can't happen in Inquisition?
For example, let's suppose that the Divine dies and her succesors are fighting for the throne. Then it would make sense for people like Leliana or Cassandra to follow the Inquisitor to save the world. Heck, as far as we know, Divine Justinia could have come up with the plan of resurrecting the Inquisition (she has been portrayed as very unorthodox), but the rest of the Grand Clerics wouldn't like the idea and try to put obstacles to the new Inquisition. Thus, it would be explained why people from the Chantry are present, why the current Chantry opposes and why in the end nothing of importance would change.