As a random aside, in your headcanon, did Cullen go to Greenfell or not?
The way I imagine it is that he spent a few months there to recuperate physically and emotionally after the events at Kinloch Hold, and once he'd regained some stability he was reassigned to Kirkwall.
Isn't it canon?
I thought Greagoir sent him there after the Blight, when mages started returning from the war, and Cullen grew super-paranoid (what if they learnt blood magic from the darkspawn???), and Greagoir decided to send him to a quiet village to guard the local Revered Mother, and Cullen spent there a couple of months. I was going to make something about his time there, and what happened, and how it helped him, but I don't have time for that anymore.
I also headcanon that Cullen requested to transfer him to Kirkwall. It doesn't really contradict the codex, because codex probably means an official paper from Greagoir, and I imagine Cullen just sent him a letter, "It's too quiet here, and I feel better when I'm busy. Please sent me somewhere where I can be too busy to think about what happened." And Greagoir said, "Ok, you go to Kirkwall, it's always busy there." And wrote to Meredith, "Hey, keep that guy as busy as you can!" And she thought, "Awesome, I have a ton of paperwork nobody wants to do! I hope that new guy has decent handwriting!"
Mages in Kinloch Hold didn't know Cullen went to Kirkwall after Greenfell, because why would anyone tell them? They probably overheard him talking about Greenfell when he was leaving, that's all. So when we hear them chatting about it a year later, it's because they think Cullen still serves there.