I think you're right and I think their conclusion is flawed. With such a massive difference between the two groups to start with, they can't claim to know with any certainty that the vaccine doesn't at least slightly increase mortality. Maybe the difference between the two groups was 82% before vaccination and 72% after. Even though that's unlikely it can;t be ruled out on the evidence so far.
But that does not mean that they claimed that "once vaccinated, your all-cause mortality drops 72%". That is simply a lie and spreading it weakens the credibility of critics who point out real problems with the so-called vaccines. It's exactly this kind of nonsense that the fact checkers love to disprove, while they ignore the good arguments.
I think we agree on a lot about this report. “Lie” is a little strong, don’t you think? It’s fun to tweak the fact-checkers (like Trump did with his misspellings, etc) and get them to highlight this flawed study. I don’t think anyone believes there was “no increase in mortality” from the vaccine. So which is it, does the vaccine help or hurt mortality? Get the report writers to defend it like you did, and in the process, expose it.