I think it's a bit presumptuous to believe that we understand perfectly what happens when an archdemon is killed. Morrigan's ritual shows very clearly that there is at least one way for an old god's soul to avoid destruction. I don't know if I buy that Dumat took over some fool's body after the archdemon was killed, but I wouldn't be terribly shocked to learn that he survived in some form. Inquisition and Trespasser have proven that Bioware doesn't mind proving that Thedosian history is wrong about everything.
Of course, we don't even know what the Old Gods actually are. If they're anything like Avvar gods, the death of an archdemon could very well simply mean that the spirit is free to reform in some manner.
Their tainted blood bound them to the archdemon, and they could hear it, feel it, as it died and was born anew, its spirit drawn to possess the nearest tainted creature. The darkspawn were mindless , souless, empty shells of flesh that could be bent and remade in the dragons image. But a man...a man's soul was not so malleable. When a Wardens hand struck a fatal blow against Dumat, the Old God's spirit was drawn not to a darkspawn but to the man who had slain him. In that moment the souls of both the Warden and the Archdemon were utterly destroyed and the dragon rose no more. The blight was over.
This is from the codex entry for the Archdemon there is little to no ambiguity or room for shady excuses.
Also Traiharder , mate i can lead a horse to water but i can't make you drink it seems.