"Couldn't believing in quantum immortality be compatible with this? You could do things like firing a gun to your head, and it would misfire every time. You could jump off a building and would land in a passing open-topped garbage truck full of soft material. You'd experience all sorts of crazy coincidences, but all of them plausibly deniable and within the framework of cause and effect as we know it."
I think one of the several issues I have with this article is that you're measuring survival in human terms, not quantum terms. One of the secret constraints in the quantum suicide thought experiment is that your method of death must be literally 100% guaranteed, and ideally for the argument, instantaneous from the point of view of your consciousness. (That is, for our consciousness's sake, I don't think Planck time is particularly relevant; more human time frames are relevant.) Sometimes this is expressed as sitting next to an atom bomb rather than just a gun.
But, even then, as a pragmatic matter, a real person trying to perform this experiment would need to be concerned about the quantum probability that the bomb does indeed go off, but leaves them maimed because it didn't exactly explode fully, but the explosives half-detonate and the uranium goes only a bit critical, spraying you with radiation and seriously injuring you but not actually killing you. As you sit there next to your quantum number generator, you are indeed systematically pruning the quantum state space of the worlds in you do actually die, but the remaining quantum state space has a great deal more than just "you get up and turn off the quantum number generator once you are satisfied".
Similarly, a gun can do a lot more than just fire and kill you, or not fire and leave you harmless. It could fire, and put what should be a fatal hole in your head, but the bare minimum quantum events occur to keep you just barely conscious.
As you prune away all the likelihoods, you're amplifying the probably of everything other than what you pruned away, not just the human-conceivable events. The harder and more successfully you prune, the weirder what's left over gets. Given that you've set up a situation in which you've got a gun aimed at your head or an atom bomb or what have you, those "weird" situations are likely to be unpleasant.
Of course, if QI and the multiple worlds hypothesis is correct, this all happens anyhow all the time, and seeing our family or friends just suddenly explode for no reason is something we are literally experiencing all the time, just with such a low probability that it hasn't happened yet. But, somewhere in the great multiverse, there's a set of people who read this message and it is immediately followed by, say, their left hand just disintegrating. Take heart... for some yet smaller fraction of you, it will also immediately fix itself.