I just think they shoot themselves in the foot by trying to make the Inquisition 100% independant from the Chantry to please players.
It doesn't make much sense in game anyway when Leliana and Cassandra go "yeah the chantry disavows us , we're heretics."
What Chantry exactly?
From the start you had Chantry folks pro Inquisition and Chantry folks anti inquisition , the last order of the Divine was to create an Inquisition and without a new one to cancel the edit , the Inquisition was Chantry approved.
For some weird reason Leliana and Cassandra are the only one mentioning the writ when it's conveniant , but at other time when you'd need it (The guy who wants to retake Haven and claims there's no papers saying Justinia approved...) , everybody has a brain fart.And the chantry sisters never bring up the subject at all nor the Inquisition for that matter.
And then at the very end , the Inquisitor has the writ in hand like it's some kind of official thing now , when the game ignored it the whole time.
I'll see if I can answer this and set some sources to it later;
The Inquisition treated the writ of Divine Justinia as official because it is official to them and it is the grounds on which they form the Inquisition. To them, it's legitimacy is uncontested but to opponents of the Inquisition it's legitimacy can be challenged especially since Justinia is not alive to confirm or deny it whether or not she dictated it to be written and the authorization of a dead woman can be called into question.
Basically, to the Inquisition, the writ is official and evidence of the Divine Justinia's approval of their organization but to others, Divine Justinia's death amongst other things calls the validity of the writ into question therefore it stops being used outside of certain situations since it can be contested and the Inquisition has a better means of securing support through the protagonist's ability to seal the rifts.
The Inquisitor brings the writ with them before the Council of Heralds because the writ is where the Inquisition claims their validity and purpose from;
"You all know what this is; A writ from Divine Justinia authorizing the formation of the Inquisition. We pledged to close the Breach, find those responsible and restore order. With or without anyone's approval." - the Inquisitor
The Chantry lost a good deal of their upper leadership at the Conclave but not the entirety of the Chantry and it is the remaining Chantry that disavows the Inquisition and their figurehead as heretical. That the Inquisition is disavowed by the leadership of the organized faith, does not mean members of the faith disavow them as some do believe the Inquisition and believe in their figurehead and so they support the Inquisition.