Hm, I think my confusion is over the idea of quantum immortality in general rather than specific to the torment scenario.

If I understand it correctly, QI says that at some point in time there will exist a single branch containing a "me" that, against all odds, never dies. The idea of quantum torture comes from noting that continuing to exist in a state of right-about-to-die would likely be extremely unpleasant.

So, what makes this single branch so important? Why is the me in that branch more "me" than a me any given branch that exists with temporally concurrence to other branches? For example, there is probably a branch out there where I am existing in horrible agony at this point in time. I don't see why we should worry about the quantum torture branch and not this branch. They both contain "me."

Basically, QI gives more importance to a "me" in a branch that is temporally isolated from "me's" in other branches. I don't see why this is the case or why time should be a factor at all.