the vision itself makes it clear that: the PC did NOT kill the Divine, or blow up the temple, vis:
1. The Divine called to her/him for help and told them to "warn the others".
2. It is clearly another entitity who has the Divine strung up and is calling for her sacrifice.
3. The PC clearly entered the room after this event had started and the Divines' and PC's words make it very, very clear that the PC had no freaking idea what was going on.
4. The entity that is killing the Divine tells his people to also kill the PC for their interruption.
Witnesses to this Vision include: Leliana and Cassandra (the right and left hands), Varric, Solas and all of the troops Leliana brought with her to the Temple.
Then the PC stops the breach from getting worse, almost killing themselves in the process. And they are the only one who can.
On top of that, Cullen and his people (if you take the charge with soldiers option)/ the scouts you save (if you take the mountain pass option) witness you close rifts and save their lives.
Leliana's connected, in most of the possible iterations of the world state. She has the ear/trust of at least Highever and the Guerrins, and also the King of Ferelden, especially if Alistair or the warden are the king/queen--and if Lel was with The warden in DA:O, even Anora partly owes her for her throne. Even if not, Nightingale has serious reach. Fergus Cousland immediately stands for the Herald. Teagan... takes more time. Also, Josephine is an incredibly skilled ambassador with connections everywhere. Cullen is still in contact with Aveline if she stayed in Kirkwall, especially if Hawke was Viscount at the end of DA2.
On top of that, people had seen "the figure" behind the PC as s/he comes out of the Fade already--there was already some rumbling as to why Cass had him/her chained up to start with. And it does take some time to spread. At first, it really is only the people who were in the immediate vicinity who believe it (indeed, the Chantry declares the Herald anathema straight away). Over the course of the game, that trust spreads, depending on how you play it.
In your comparison, it's like the cops found a video that proved the guy didn't kill those kids after all.