If QI is true, I expect to observe myself surviving. If QI is false, I expect not to be able to observe anything. I don't know exactly what that means, but I don't feel like this confusion is the problem. I think that surviving thousand-to-one odds must be strong evidence that I am somehow immortal (if you disagree, we can make it 3^^^^3-to-one), and QI is the only form of immortality that I currently assign non-neglible probability to.

I briefly thought that this made QI a somehow priveleged hypothesis, because I can't observe the strongest evidence against it (my death). But I don't think that's the case, because there are other observations that would reduce my belief in QI. For example, if wavefunction collapse turns out to be a thing, I understand that would make QI much less likely. (But I don't actually know quantum mechanics beyond Eliezer's sequence, so the actual observations would be along the lines of "people who know QM saying that QI is incompatible with other observations that have been made, and appearing to know what they're talking about".)