I seem to recall one of the Devs or the Producer confirmed that basic premise more recently. There is a peace conference. The Chantry leadership is decimated and events follow on from that. However, we have been assured that we are not part of the Chantry itself, nor obliged to follow its lead. So I'm thinking that after the previous attempt on her life Justinia makes a contingency plan should the next attempt succeed. She is something of a reformist, with a shady past and a propensity to forgive sinners, and so not popular with Chantry hardliners from the beginning. Her attitude towards mages would not endear her either. So I imagine she would expect further attempts on her life. Holding the peace conference at the site of the ashes was probably because she thought no one would be sacrilegious enough to defile such a holy place.
Even if she had negotiated a peace, it might well have needed some muscle to push it through Thedas wide. There was also a problem highlighted in Masked Empire that nobles kept a bit uneasy if the Chantry appears to be wielding too much secular power, so the Inquisition was her way of doing this at arms length so to speak. It was originally set up to at least "appear" that it was independent of the Chantry. This means the structure would be there to continue with its purpose even after her death even if a new Divine was elected and failed to take action. I'm assuming she chose to take the name of the former organisation because at the time its basic purpose was to deal with the chaos that existed in the aftermath of Andraste's death and the reduction of the Tevinter Imperium's power. That organisation was independent of the Chantry because there was no Chantry at that time, nor a unifed Andrastrian religion, but just lots of cults.
That's my take on the information that we have been given thus far but no doubt all will be made much clearer after the Big Bang at the beginning of the game.