I'd like to bring Sandal to this discussion since he propably posesses the same kind of power that Valta gained after she was hit by pure lyrium, his is propably just much stronger.
I recalled that scene from DA:O in Fort Drakoon where Sandal had darkspawn blood all over his face but he never suffered from the taint.
Could that mean that the (re)connection the the Titans does make dwarves immune to the blight? I'd really like to know if the Sha-Brytol are immune to it too, would make sense since the darkspawn in the deep roads seems to avoid Titans.
That theory of "living" Titans granting immunity to the taint leads me to the wild thought that the blood of slain Titans (slain by Mythal and maybe other Evanuris) could become red lyrium and that might be the origin of the blight.
Here two codex entries that support this idea:
"What the Evanuris in their greed could unleash would end us all. Let this place be forgotten. Let no one wake its anger. The people must rise before their false gods destroy them all." (DA:I, Trespasser)
"The Stone bears a corruption as old as balance." (The Gangue Shade, DA:O)
An interesting theory I've read on another topic was that the Evanuris' purpose behind the Vallaslin tattoos was to bind the elves to the physical world so they can no longer enter the fade and thus make them slaves/easier to control. And since Vallaslin contains lyrium - lyrium they mined out of the Titans - It only makes sense that Templars also use Lyrium to bann magic/strengthen the veil. Just mentioned this cause it gives a good reason why the Evanuris are so interested in the Titans.
However I have no idea how the taint in the Black City, the Magisters and the Archdemons fit into my dead Titan theory. I cant imagine that the Black City is a dead Titan that was somehow locked away, almost unreachable in the fade.