Also, on a different note I do have an argument about sending away Cullen as well...
We know that Greagoir sent Cullen to Greenfell to recover first (and that's what I meant when I said he was at least trying to help), and only then to Kirkwall, because he thought Cullen may still blame the Fereldan mages for what happened to him. We don't know if Greagoir had many options about Cullen's new appointment, maybe it was just Kirkwall or Ferelden (after all Kirkwall is the closest place with a Circle; or maybe Kirkwall just had a vacancy). Maybe Greagoir also thought Cullen would feel safer in Kirkwall, because the rules there were more strict. I don't believe Greagoir wanted to get rid of him, because one of the possible epilogues in DAO was that Cullen replaced Greagoir eventually (which can still happen, btw

), and I don't think Greagoir would have allowed it. The retiring knight-commander probably can suggest the candidates for his replacement. I'm pretty sure he could have ruined Cullen's career if he wanted to, but Greagoir doesn't seem like the type to me.
Regarding trusting Irving - like Cullen said in DAII, that's what being a templar is about (it seems to me like he got it from Greagoir, because the situation is too similar). You have to take that risk, or you may kill an innocent. I think it's the kind of attitude every templar should have. But it's not Greagoir's choice, btw. This is one of the difficult decisions, which the Warden makes, not Greagoir. Because the Warden and Wynne saw what happened inside, and Greagoir can only trust their judgement. He can't trust Cullen, because Cullen is too traumatized to judge clearly, and Cullen didn't see everything, he was in the cage. That's why Greagoir trusts the Warden. The Warden - because that's what you represent with the treaties, that's why everyone has to listen to you and do as you say. And if the Warden says Irving is not possessed (and to ensure that we were using the litany of Adralla), and if Wynne confirms that, Greagor has no reason to mistrust Irving. I think it's great that they cooperate like that in Fereldan Circle.