Personally, I'm more partial to the idea that the Old Gods are the Forgotten Ones
I believed this too when playing DA:O, but since Inquisition, I'm not so certain. Cassandra's banter with Solas regarding the Old Gods possibly being pets to more powerful entities and Morrigan's claim (after drinking from the well) that Corypheus was attempting to replicate the "gods of old" when he imbued a dragon with his essence makes me believe in the 'Old Gods as the Creators' pets' theory in which each creator had a powerful dragon minion imbued with part of their soul. Kieran could thus be Flemeth's attempt to free the essence of one of her comrades (possibly Ghilan'nain who I believe to be the equivalent of Urthemiel) from the taint.
I do not believe that the Old Gods were the ones responsible for sending Corypheus et al. to the Black City: I believe that that was a ploy by the Forgotten Ones to bring the taint into the mortal world and that they were manipulating the magisters by posing as Old Gods or Corypheus simply believed that the voices he was hearing were those of Dumat even when they weren't. The Forgotten Ones are certainly linked to the taint in some way: Andruil appears to have become tainted after hunting them in the Void (which was worshipped by a Nevarran cult that revered the blight). This would suggest that they are the reason that the Golden City was blackened and the ones behind the original red lyrium as discovered in the Primeval Thaig in DA2. Their goal is to spread the taint and battle the creators who are their old enemies (by corrupting their dragon pets and turning them against them and by tainting their eluvians). Interestingly, Corypheus' "claw of Dumat" statue is identical to statues found in the Primeval Thaig. In the codex entry on said statue, it specifically mentions that Corypheus at the time he brought it into his estate was hearing whispers in his sleep, and yet after he was corrupted and separated from this statue, he hears nothing (as stated by him during Calpernia's quest).
So methinks that this 'claw of Dumat' has nothing to do with Dumat but is in fact a conduit from which the Forgotten Ones can issue commands to mortals - just as they did to their followers in the Primeval Thaig.